Corporations are like guilds, but with many more features to organise them. There is no problem if you pick one that doesn't suit and need to change. Corps will have some kind of tax, perhaps 5% of your earnings from some activities, perhaps also a flat-rate per week.
PvP corps will have ways to cover cost of lost ships during sanctioned PvP operations, so you can enjoy it with less fear of financial loss. These corps also should have an industrial interest to manufacture ships and weapons.
Really, Eve cannot be enjoyed to its fullest outside a Corp. You should join one.
There is an in-game channel called Recruitment you can join.
There is also a web forum here which includes advertisers. That's how I found my Corp.
A new site eve-careers also links players with Corps, read about it here.
There is an in-game Corporation you can join called the Eve University. All reports on it are good. It's a truly helpful group of people who just want to give noobs a grounding in how to play Eve. Learn more about how to join here. Like other universities, they also do a number of silly things to amuse their members.
Another Corp, Agony Unleashed, have a paid-for PvP training regime you can read about here. Agony is currently the only corporation that trains non-members, which can be useful, since there can be a significant downside to joining a corp.
To actually join, you do not get sent an invitation when it suits you. You have to fly to the Station with an office or HQ of the corp and sign up there. After filling out the application, invitations are sent electronically and you can accept from where-ever you may be. However, don't just pick a corp out of an office and hit 'apply' - do your homework and find a good corp, get to know the members, then join.
Update July 7: it's possible that joining a corp is easier now. Rev 2 apparently made some changes. I'm going to test it shortly and update this paragraph.
A really important feature of Eve, which makes Warcraft guilds look even more pathetic, are Alliances. Corporations can band together into an alliance. You get a shared channel, enemies, combat and trade benefits.
Alliances are the unit that defends regions in 0.0 space against other alliances. When you join a Corp, you join its alliance automatically, and you will also gain all of its friends and foes.
You should check my maps page for pictures of how much control each alliance has.
More detail on Corps
The below content came from a great forum post.
1) Corporations do whatever they want to do. There are all sorts from small to large, hi sec to no-sec, PvP to Carebear, roleplayer corps to shell corps. You name it there is one out there that does it.
2) Corps need people more than people need them. Indeed a corp is nothing more than the collection of people who belong to it.
3) Some welcome noobs. Some don't. Requirements for joining are as varied as there are corps.
4) There are not too many scams perpetrated on noobs going into corps. But they exist. There is no legal judge and jury to protect the innocent! Do not pay to join a Corp! That's a scam. You might be expected to do some 'slave labour' to earn your way, so just decide if it's worthwhile. Don't put any of your own money or ships at risk beyond the taxrate, until you've verified it's a totally legit Corp.
Corps are truly the road to a more full experience of Eve. Together you can definitely achieve more than alone although going solo is certainly possible. Eve generally has some great members and while there are jerks here and there (as anywhere) they seem fewer and further between in Eve.
Ask questions, ask about their expectations from you. Ask about their policies (e.g. stance on pirating, reimbursement policy, time online reqs, voice chat necessary, corp taxes, etc.). Are they at war? Do they go to war a lot? Anything else you can think of.
And of course if you make a mistake you can always leave. Just try not to corp hop too much (some is to be expected) as future corps may wonder about that.
The downsides of corp membership
Under the social rules of EVE, corps are held responsible for the behaviour of their members, and members are held responsible for the behaviour of their corp. This means that if a member of a corp steals from someone, your corp can very quickly get a reputation for harbouring thieves. The same goes for acts of piracy, fraud, deception or rudeness. Rudeness can and will get you killed in EVE (especially outside highsec), and it can get your corpmates killed too.
Inside highsec, corporations are more vulnerable to violence than individuals. For 50 million isk (pocket change for an established pirate corp), a hostile party can issue a war declaration. This is essentially a bribe that makes CONCORD look the other way while the corporations blow each other up. War declarations have been issued due to rudeness, harbouring thieves, pirates or frauds, and for some less savoury reasons as well. An established money-making tactic is to declare war on a corporation, then demand a fee to withdraw it again.
Tips for identifying a good corp (thanks for these, Shanur)
- Distinctive value. A good corp has a clear vision on what it wants to achieve in the game, how it wants to go around to doing this and what it is prepared to commit to get the means to do this. Generally you will have a specific style of playing that appeals more to you than other styles. Look for a corp whose visions and strategies match your preffered style of playing the most. Even if they are not the best, at least they will cater to you enough that you should enjoy your time with them.
- Property and trust. Before joining any corp, ask yourself this: After speaking to the CEO or director, do you trust the corp enough to risk losing a big part of your personal assets due to their actions? Corps work most efficiently when resources are shared to a high degree. As such, trust is very important. Do you trust the people in the corp? Also see what sort of resources they have. Their ability to be worthwhile for you depends highly on what they have in the way of industrial backbone, territory and other infrastructure. Do not ask about rights to manipulate corporate assets. That is by most recruiters interpreted as you being an enemy spy planning to steal from the corp.
- Organization. Should be straightforward for a WoW player. Are you joining a rabble of independents or a tight knit well organized team? This also covers diplomatic relationships they might have with other corps and alliances. Friendships and enmities will affect your game significantly.
- Protection. As a corp member you will be a war target. It's only a matter of time. Does the corp have a military arm to protect your hauler? If you are a military player how much of your time will you be expected to fly escort for your corp mates? Does the corp have an agreement with other military or mercenary corps they can appeal to for protection? These relationships also include to what extent the corp has undisputed access to 0.0 space.
- Benefits. What you can do for a corp is usually pretty straightforward. What the corp can do for you in return is an entirely different matter. Will they offer ships and equipment? Profit sharing? Joint ops? Cheap refining? And how do they achieve these things? Do they have their own industrial backbone or do they rely on pacts or their alliance for that? Even a military alliance generally has some form of industrial backbone to cover replacement of their lost ships. Find out if the corp you want to join has as well.
- Reputation. Tricky. Typically a corp recruiter will not give you a satisfactory outline oftheir corps reputation. Partially out of pride, partially because they may not be fully aware of how others regard them. Best you can do is see if the corp discussions forum mentions the corp you want to join and in what kind of light they are held there. Also ask your recruiter about controversial activities. How are their views on piracy? On scamming? On podding? If they own 0.0 territory, do they use NBSI or NRDS? Do they have sworn enemies? All these should give you an idea how people will regard you once you join.
Starting your own Corp
Starting your own corp is difficult. Really difficult. Really really difficult. Which is to say that it's hard. Feeling discouraged about starting your own corp? I hope so.
In this lively discussion about whether newbies should create corps or not, Shanur outlined the problems you face as the CEO of a corp:
1. Your corp will be one among many. You need to have a plan to distinguish yourself from all those other corps, or no one will consider joining you. This one is a consideration in most games, only in EVE it tends to be more punishing due to some other considerations.
2. Your corp is a legal person. It actually owns stuff. Because however this stuff needs to be accessed by human beings to be put to use, it can be ripped off. Corp theft is a major issue.
3. Corps are expected to be self regulated. What this means is that where in other games you have the game itself force people to be nice to each other, in EVE all you have is trust, access rights and the ability to shoot each other. This immediately puts a bigger strain on organizing your operations (groups) better than you would in "that other game" because otherwise you will have people hogging all loot and then be shot by the rest after which all out brawls for the wreckage occur.
4. You are always open to attack. All corps, regardless of where they are located, are vulnerable to a form of non consentual PvP combat, war declarations. This means that even if you dedicated yourself to being an industrial specialist, unless you arranged for some military means to ward off raiders to your mining and cargo ships, the only place you can hide at is inside a station and prey your enemy is just after your loot, meaning he'll grow bored and cancel the dec eventually. This will prevent you and your corpmates from playing the game, however, which has in itself caused many corps to disintegrate just so people could get out of the war.
5. You have to provide. Historically, by far most people join a player run organization because they expect it to better them. Usually because it gives them a shot at loot they could not hope to obtain on their own or with a randomly recruited team. In EVE too, people will expect there to be tangible benefits, other than the friendship of your corp's members, to be offered in return for their support. Not only do you have to think up what you'll offer (collective income, ship replacement, low cost high efficiency services, etc...), but also how. You will find that in order to offer your members these benefits, it is inevitable that you have access to some form of industrial means. Even the most hard core pew pew corps either have struck up arrangements with industrial corps (usually in the form of protection vs profit sharing pacts) or have fallen apart from lack of means.
6. You are being tracked. Every corp you have joined is permanently stored on your character's record, making reputations matter even more than in other games. In WoW, going inactive for a few weeks, or just keeping out of trouble and then singling out newcomers was usually enough to get rid of any bad reputation and go right on what you were doing. In EVE, even joining a badly reputed corp like Goonswarm by mistake will haunt you for the rest of your characters existance. It's all there in white and stylesheet color on your corporate history tab. What this means is that people will be very critical of joining a corp and reluctant to join one they do not know yet due to it possibly harming their reputation. You will have to profile yourself to be appealing to at least some groups within EVE or you will have serious trouble thriving.
There are alternatives to creating your own corp. You can create a custom chat channel and mailing list. You can be a group of friends inside a larger corp. If you really want to create your own corp, then go read the CAOD (Corporations, Alliances and Organisation Discussion) forum for a bit. Read some of the threads by new CEOs talking about how they got scammed and/or wardecced. Read the responses from the veteran players that talk about how they could have avoided this problem, and what to do about it. And then (since you're obviously determined to do it), good luck.