Yes, the proving process takes place at registration. The id (driver's license) is proof that you're the person signing the registry. The move to require this in more states has been undertaken by the Republican party because of who will be most adversely affected by it. It is similar to other voter schemes that were drawn up in the South to disenfranchise black voters, similar in that people in certain economic strata would have greater difficulty meeting the requirements.
However, contrary to certain assumptions made above about the so-called "disenfranchised", this does not mean they are not able to make a logical decision between political choices, nor shouldn't be afforded the right and opportunity to make one.
Fact is, if there is anything that the Republican primaries have proven it's that having one's proper papers and an id does not make one intellectually superior or more adept at discerning fact from PURE bullshit.
As I said earlier, the efforts of conservatives to eliminate voters from the registry should only serve as greater impetus to get out there and register, obtain whatever necessary documentation, show up at the polls in hordes, and vote the fuckers into oblivion.