If you received a Google wave invitation, and just created your account, here's the first thing to do: Add some contacts!
Look down at the lower portion of the left panel, and you'll see the Contact Box. Click on the + sign, to the right of "Manage Contacts" to add a new contact.

You will need to ask your friends and family for their googlewave addresses, the same way you have to ask people for their email addresses when you first get acquainted.
Type in the person's googlewave address, and click Submit.

Now the person shows up in your Contact List.

Click on the person's photo or avatar to bring up a dialog box. Click on "Ping" to send the person a message.

Type something in the message box and click "Done."

The ping becomes a new wave that will show up in the center column when the person goes to Google Wave. The person will not get a separate email notice, so you need to count on your friends to check their waves daily, just like you count on them to check their email messages. You could send the person an email saying "Hey I waved at you, check your waves."

The wave is private between you and that person, unless you decide to make in public. Here is how you make it public.
You can also keep the wave private, but add other participants. To add another participant, click the + button in the left column, above the wave content.

Your contact list will pop-up. Just click any name in the contact list that you want to include in the wave.

Do you ever have email conversations with groups of people? Maybe your team, office staff, and assistants? Or maybe you send emails to a group of family members, and everyone chats back and forth via group email.
If you think in terms of using Wave in those group email situations, you will have made the basic Wave Paradigm Shift.
Cheryl - I am so jealous. I want a Google Wave invite too! I'm saving this post for when I am a waver too!