This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
If you actually have you code in an Action class then have your "ActionLister" call the Action instead, then you can also add a FocusListener, which is needed to capture if the user has left the TextField, can also call the Action too, therefore reusing the Action class and not having duplicate Code.
You can also implement a KeyListener for getting which key is pressed, but I think the functionality you are looking for with Return and Tab is best implemented in the FocusListener instead, maybe.