Everything runs from the web -- you just need a browser to make it work (no complicated desktop software like DreamWeaver)
There is a markup language, but it's easy to learn and there are GUI buttons to help you
Many different implementations exist. Many are free. Also there are commercial companies that host everything for you (e.g., http://www.wikispaces.com, which has free basic sites for educators)
Ways to use Wikis
Just use it for your own web sites -- it's a great way to build a web site (easy to get started, easy to update); e.g. this site, http://www.cs.uml.edu/ecg/ (Fred's research group)
Course web sites, especially ones where students will contribute. UML examples: