Is this a Windows application or a Web application? If it is Windows app, use Sendkeys to send an Enter to the textbox. If it is Web app, it is a less straightforward and I would need more information to help. (You can do a Sendkeys to the browser but that is not guaranteed to be an enter to your field, you can do RaiseEvent but sending an Enter is not an option.)
For your button, PerformClick should do the same thing as clicking manually.