If you're anything like me, you've probably been so anxious to finally get your Google Wave invitation, once you do get it, you don't know what to do.
Depending on how many friends you have added to your Gmail contacts and how many of those have a Wave account, you may not have anyone with whom to speak.
Understand your contact list is exactly the same as the one you see in Gmail. However, you only see contacts who have Wave accounts. If you see few to no people in this list, try a search (the text box next to the button "New Wave") for "with:public" these searches are case-sensitive, so enter this in exactly as you see it here.
You'll find a lot of the publicly-viewable waves are cluttered with hundreds of people, so you may want to narrow this down as "with:public vegan" to find vegans or "with:public omaha" to find friends waves about Omaha.
There are two robotic entities to Google Wave: bots and gadgets. Bots are added to your waves like users. They have their own profile pics and @ addreses (only "@appspot.com" instead of "@googlewave.com") Bots can be programmed to search the contents of your waves and perform certain duties. Here's a few bots you can add right now:
SweepyRemoves empty blip waves
sweepy-wave@appspot.com
TwitusernamesTurns "@user" syntax into twitter links
twitusernames@appspot.com
Puts feeds into waves
rssybot@appspot.com
Eliza the Robot ShrinkAn artificially-intelligent bot with whom to have a conversation
elizabot@appspot.com
Gadgets are very similar to gadgets in iGoogle. Gadgets are embeddable interactive media for your waves. These can be games like Chess and Sudoku or utilities like trip planners. See this link for a generous list of popular gadgets for Google Wave.
Users who were invited to Google Wave from another user may not yet have the ability to send out invites. However, if you were signed up for Google Wave all on your own during the signup period, search your inbox for "invite". You should see a wave there titled "Invite others to Google Wave." Open this wave where you may invite up to eight people.
Take advantage of Google Wave's collaboration potential, even if you don't have a lot of contacts with whom to collaborate. To make a wave public, simply add the bot "easypublic@appspot.com" to your wave contacts.