Unfortunately, it is not possible to join a particular Public League. If you want to compete against your friends/colleagues, you must create or join a Custom League.
If your friend has created a Custom League and you've received an invitation to join it, please go to the Yahoo! Sports Fantasy Football home page.
First, click "Sign Up." Then, click "Select" under Join Existing League. Next, click "Select" under Join a Custom League.
You're then prompted for the League ID# and Password forwarded by the league commissioner. If you don't have this information, you'll need to contact the league commissioner.