Anyone know how to get on civilian deployments?

Depends what your job is. If you want contractor jobs, see SSG Toryn Green's post. You can also scour fedbizopps at fbo.gov and see if any contractors are getting awards for contracts downrange, and then look at their website for openings. Federal agencies will deploy civilians too, I'm guessing DoD agencies or Department of State probably deploy the most. Good luck. When I was downrange, looks like they were making good money.

I would recommend checking clearance jobs.com and checking with the contract companies such as Fluor and Dyncorp. There's definitely openings, just depends on your experience and where you want to go.