I applied through an employee referral. The process took 2 weeks. I interviewed at Environmental Protection Agency (Dallas, TX) in May 2015
Interview
There was no interview, they saw my resume and accepted me. There are no official intern positions, you just have to ask the right people. Like I said, no expectations of interns or any competition. Security clearance took way longer than necessary too. Your mileage might vary in other regions though, I think Region 2 is more competitive.