Starting to develop on Google Wave is easy. You don’t have to install anything, except you need a “Modern Browser” like Firefox 3.5, Chrome, Opera or Safari. You can just login and start experimenting. You need an sandbox account, that you have to register for here.
The best presentation is probably the Google IO keynote found bellow. This gives a great introduction to how wave works.
The best place to start is the Wave homepage http://code.google.com/apis/wave/
There are some nice tutorials of the different types of components, which can be developed using the different Wave API. There are the following types