I have tried numerous things and I keep wasting kits with no apparent change in the condition of the weapon I'm trying to repair, so obviously I'm missing something. Please advise. Thanks!
As mentioned, you just need to equip the weapon you want to repair and then use it as you would any other aid, and you should notice the condition of your weapon raise. Last I read, regardless of your repair skill each kit raises the condition of a weapon 25%, so 3 or 4 would bring a weapon to 100% (and will, I've created probably 15 or 20 by now and use them all the time).