Here are a few examples from the Google Wave team about how to Google Wave:
UPDATE: Lars Rasmussen at Google also links to a number of examples on how to use Google Wave in a recent post on the Official Google blog.
Keep a single copy of ideas, suggested itinerary, menu and RSVPs, rather than using many different tools. Use gadgets to add weather, maps and more to the event.
Prepare a meeting agenda together, share the burden of taking notes and record decisions so you all leave on the same page (we call it being on the same wave). Team members can follow the minutes in real time, or review the history using Playback. The conversation can continue in the wave long after the meeting is over.
Group reports and writing projects
Collaboratively work in real time to draft content, discuss and solicit feedback all in one place rather than sending email attachments and creating multiple copies that get out of sync.
Bring lots of people into a wave to brainstorm - live concurrent editing makes the quantity of ideas grow quickly! It is easy to add rich content like videos, images, URLs or even links to other waves. Discussion ensues. Etiquettes form. Then work together to distill down to the good ideas.
Drag and drop photos from your desktop into a wave. Share with others. Use the slideshow viewer. Everyone on the wave can add their photos, too. It is easy to make a group photo album in Google Wave.