The current situation is that you can play international rugby for a country on the grounds of birth, residency [3 years I believe] or parental or grand-parental rights.
Thus the current crop of internationals Manu Tuilagi, George North, Quade Cooper, Matt Stephens, Dylan hartley, Luke Charteris, one of the Franks brothers [etc] all play for countries they were not born in.
A few years back the situation was a lot looser with Jamie Salmon [NZ + England], Shane Howarth [NZ + Wales] and Frank Bunce [Samoa and NZ] playing for two countries. This is no longer allowed, once you have elected to play adult international rugby for one country then you may no longer qualify for another.
Also, after the "grannygate" scandal of the early 2000's, qualification has been tightened up. Before that hardly any checks were made. I once asked Damien Cronin what was his qualification to play for Scotland. His answer - "my grand-mother's got a scottie dog".