I pulled up the official Wisconsin site, one of the first states brought up in your "news" source (John Oliver). It is very easy to get an ID, and it's free. I would suggest accessing additional news sources, if you want to be properly informed. You can access other state websites if you like.Thanks, yep that is the one. The funny kicker there is how GOP law maker caught on tape casting his vote and then voting again for a missing colleague.
http://wisconsindot.gov/Pages/dmv/license-drvs/how-to-apply/petition-process.aspx