What we do now works fine. Numerous studies, including by people that had a strong interest in wanting to find problems, have found that the amount of ineligible voters that slip through is insignificant.

Voter registration records are generally public and are scrutinized by partisan organizations that want to try to disqualify voters that they think will vote for a different party.

The voter ID laws Republicans are trying to pass would stop at most a negligible amount on ineligible voters, but would also disenfranchise several million citizens, most of whom are poor and/or elderly and/or minorities.

If Republicans would propose a voter ID law that also includes funding to provide free IDs to every citizen who does not have one (including covering the costs of obtaining the necessary documentation for those IDs), then most people objecting to the current proposals would drop their objections.

The same way we do now, checking their voter registration. Voter fraud isn't prevalent enough to require overhauling major systems and policy.