You have two choices: Put a rack on top of the car, or on the back of it. The trouble with the back rack is that the Civic is so low to the ground, it聮s going to take some work to ensure the bike wheels aren聮t scraping the ground behind you. The trouble with a top rack is expense. By the time you get the crossbars and the bike trays and everything, you聮re into it for $400 or so (maybe more than the Civic is worth).
Saris Bones 2-Bike Rack

So I聮d get a trunk mount and hope for the best. Performance聮s XPORT Porter Trunk Rack ($60; www.performancebike.com) is pretty much as its name implies聴a two-bike rack that attaches to a sedan trunk with various nylon webbing straps and cushioned contact points so you don聮t mar the paint. The Saris Bones 2-Bike Rack ($120; www.saris.com) is a little more elegant-looking, with a design that arches from the trunk lid to the bumper, and the capacity for (duh!) two bikes.
Alternatively, you can check in with your local tow-hitch outfit and see what it would cost to have two-inch receiver hitch bolted or welded to the Civic. It聮s doable, I know that, and likely will cost $150 or so. Then you can get a receiver hitch, which has the advantage of allowing the trunk to be opened and closed without taking off the bikes and the rack. Performance to the rescue here, too, with the XPORT Free Loader, a three-bike hitch rack for the budget price of $80 (it聮s on sale now, regularly $100).
Check out this year聮s more than 400 must-have gear items, including , in the 2006 Buyer聮s Guide.