I personally strongly support the Australian method. Make voting mandatory. I'm sure some morons may think that "fascist" or something, but it's objectively the most democratic way to do it.
Don't even need to do that. Oregon uses postal ballots and they had 80+% turnout in 2000, 87% in 2004, 85% in 2008, 82% in 2012. That's pretty high, compared to the national turnout of 30% lower in those years.
http://sos.oregon.gov/elections/Pages/electionhistory.aspx