From the Home screen, tap the Menu key > Settings > Add account (under the Accounts section) > Google > Existing.
Enter your email address and password, then tap the Next icon .
Once you've set up your Google Account on your phone, it'll automatically be synchronized with your Google Account on the web (depending on your synchronization settings).
After signing in, you can use Gmail and Play Store; back up your settings to Google servers; and take advantage of other Google services on your phone.