The solution is to catch each keypress as the user types text into the box. If and when the user presses the Enter key, simply call the same subroutine that would be called if the user had clicked on the button.
Code:
sub Textbox1_KeyPress( pKey )
if pKey = Asc( 13 ) then Button1_Click ' 13 = the Enter key, if I remember correctly
end sub
sub Button1_Click
msgbox( "Hello, World!" )
end sub