My friends and I were thinking of starting our own wiki. Given how widespread they have become recently, we heard it isn\'t that hard. We want to keep the site as simple as
I'm guessing from your question that you mean for personal, instead of business, use.
As Bayard implies, the key to success is the social side. For the technical side you'll need to have a server (or someone prepared to host it) and good wiki software. The most obvious choice here is MediaWiki which is well developed (features), well tested, well known (through Wikipedia) and completely free. Furthermore, it can easily be extended with a variety of new features (extensions).
Take your time making the choice of software because it is hard to change later. WikiMatrix may help here (to compare software).
However, the social side is also important. What is your topic? Why is it necessary? Could you accomplish the same with Google Docs (if it is just for friends) or do you want a wider involvement?
If you want a wider involvement (e.g. allow the public to contribute), then decide whether you will permit anonymous edits.
Now the most important: moderation. This means (1) you need clear rules (like who can delete pages and what the process is) and (2) someone (or, better, a group) to enforce those rules (the moderators). You will need to create the right balance for you in terms of being strict with the rules (encourages quality) and being flexible (encourages participation).
You will also need someone to take a lead - to encourage, support and manage the moderators and processes. This person is often called a wiki champion. Here's a good link explaining more about this role.
Final tips: be clear what should go onto the wiki and what not, stay close to your users (customers) by encouraging feedback and keep it fun for everyone!
Later addition: check out these Stack Overflow questions and answers:
Another edition: make sure the moderators create and maintain great "how to" pages for the wiki. Often they are not intuitive (especially for people used to Word). You might want to start with a "What is a wiki?" page - and then, after a brief introduction, link to a Wikipedia page all about wikis.
The most difficult part of implementing a successful wiki tends to be social, rather than technical. Wikipatterns is a good resource which describes the challenges you're likely to encounter.
MindTouch has a free, open source wiki (http://www.mindtouch.com/downloads) that sounds like it would be perfect for what you're trying to do. I've used it in the past and it's super easy to get up and running and very flexible. Watch one of their demos before you make any decisions though (http://www.mindtouch.com/support_and_services/demo_videos).