Measuring a capacitor requires sending it an AC signal and checking its reactive impedance against a known value. There are specialized testers and there are also programs for the PC that will do this. But in your situation - if you suspect the components are in bad shape - I think you'd be better off getting some brand new high-quality caps and rebuilding the crossover.If the problem is that you don't know what values you've got, then you may want to do some research. The problem is that measurements of the components in the circuit might not give conclusive results. If something is defective, then measurements aren't going to give you the information you need.
About prices, the thing is that a decent crossover capacitor is easily $2.00 to $5.00 for medium values that are common in passive crossovers. Coils are from $2.00 to $20.00. That's not the high dollar stuff either, it's just Dayton or Solen polypropylene caps and stuff like that. Good parts, but not the really expensive stuff. So you can see that cost of parts is probably at least $50.00 or $100.00, maybe more.
If you're on a budget then maybe a complete rebuild isn't necessary. Or if you want to tinker, that's cool. Maybe you can replace parts one at a time to find the ones that are bad and stop when the problem is fixed.
But if you really think the crosover components are bad, it's a simple enough circuit that an entire rebuild is a fairly trivial task. It's like an engine rebuild when a motor gets old - You may only need to replace rocker arms or lifters to make the engine operational, but the rings aren't sealing as well and the bearings are worn. So that makes a complete rebuild attractive to bring an old engine is back to 100% performance.