Do you have your Gmail set up on your email application or Gmail application? I think if you have it set up on your Gmail application, a popup with show when you try to access your mail saying the username and or password is incorrect and at that point it should have an option to put in your new password.
If you are using the email application, go to your email, menu, more, settings, account settings and change the password there.
Found it, A warning kept coming up on the status bar at the top, I would select it and it would just go away, finally after about the 4th time when I selected it it brought me to a place to put in the password.
Another thing you can do if it happens again, sometimes it's stubborn like that, is the following,
Settings > Accounts & Sync
Disable Syncing for Google. Then re-enable Syncing, it should ask again.
In the event the popup doesn't come up and no amount of waiting results in a popup,
Settings > Accounts & Sync > Google Account
Click the Remove button at the top. Then re-add the account and enter the new password.
Option two is typically a last resort, as the popup should appear when it does it's regular sync, a force sync or the disable/re-enable sync option I describe above.