Do some part comparisons on
www.hondaautomotiveparts.com If they have the same part numbers between the CRX and the Civic, then you're good to go. I'm pretty sure all of those parts are the same with the exception of the sway bar. Sway bars came in a few different diameters. You maybe want to check that out thoroughly.
Since you probably don't have all the tools, the first attempt at this is probably going to feel like a bit of a gong show as you go back and forth to the auto parts store to pickup the tools you need.
First thing you need is a factory service manual. It has diagrams and all the nut and bolt torque values. If you need descriptive help on dismantling and reassembling the suspension, let us know. I've completely ripped apart and reassembled the front suspension on several 88-91 CRX's.
You will also need:
-Cotter pins for the castle nuts on the balljoints
-Anti-seize compound
-2 pickle forks for separating balljoints (one for lower balljoint, the other for tie rod end balljoint)
-Grease for the pickle forks so you don't tear the balljoint boots. If you do tear them, just replace them and pack them with new grease.
-Rust penetrating spray for all the stubborn bolts. (you may also need a small propane torch if they still won't come loose. Be careful not to torch your rubber bushings though!)
-32mm or 1 1/4" socket for the axle nut.
-Long breaker bar for the axle nut. (I use a 24" breaker bar with a piece of pipe over the handle to extend it to 36")
-A pin punch and hammer to knock out/pound in the little tab on the axle nut. Depending on the condition of the axle nut, you may wish to replace it.