If you're anxious to see Google+ in action, you – like everyone else – need to wait for your invite. Of course you can fill out a form to request one, if it works and doesn't give you an error. Google is very careful about what kind of access they give out before products hit their prime (even if that prime still means beta).
While others are kicking the tires, you can peek through the fence to try to get a look. If you have a Google Profile, you're halfway there. When Google refines whichever pieces are not done, your profile will look very similar.
Google has a new search parameter to allow you to search for people that have plus pages (or profiles which seem to be similar, but not searchable). The search parameter is: tbs=prfl:e.
Adding that parameter to the end of a Google query (in the command URL, not in the search box), will allow Google to return only Google profiles in the results. Note the addition of the "With profiles" box, which can be removed with the "x". Doing so allows you to find people who are already using Google+.
The URL for Google+ users takes the format plus.google.com/(some number). That number represents the individual user.
If you have a Gmail account, you can find this number by signing into your Gmail account and viewing the source code of the Web page in your browser. Search the code for ManageAccount?. The next line of code should have a long, 21-digit number in it. That is the number by which Google identifies you. Use it to preview how your profile might appear.