The best, easiest, and cheapest solution is what California (mostly), Oregon and Washington already do—vote by mail. Ballots are mailed out to the homes of registered voters several weeks before election day, voters fill them out, and either mail them back in or drop them off at select drop boxes if you don't trust the USPS. Oregon has had this system since 2000 with zero problems.

While Ohio's Republican leadership has done much to try and restrict early voting, it is also aggressively promoting its vote-by-mail option. Thirty percent of Ohio voters voted by mail in 2008, and all Ohio voters will receive an absentee ballot application in the mail this year...

But if you're not going to do vote-by-mail, Virginia shows how a voter ID law can be inoffensive.

If you show up without proper ID, you can vote provisionally, and you then have three days to come up with proper ID. And you don't have to show up in person to prove your identification. You can email, snail mail or fax the proof.
You don't need a photo ID. Acceptable forms of ID are: driver's license, school ID, employee badge, utility bills, paychecks with an address, bank statements or a special voter ID card. Pretty much anything with your face and name, or name and address.
A voter ID card will get mailed to every registered voter in the state. If you register, you get your card in the mail.