Go to Settings > Accounts and sync. If your Google account is listed there, make sure auto-sync is turned on. If the account is not there, add it.
Then open your Gmail App, hit Menu > Settings and click on that Gmail account. Go through the account settings and make sure your Notifications are set how you want them (ringtone, vibrate, notify once or for every email).
Also, if you use Labels in Gmail, hit Manage labels in the settings to make sure all of the ones you want are set to sync.