I'm rebuilding a Stratocaster, and I put a new pickguard in that's a a very basic wiring setup for a strat: a single humbucker and a volume knob. I have my ground wire soldered in the back. Soldered to the volume knob and my live wire is the volume and the input jack. But when I plug in, I'm still not getting any sound from my strings - although there is a slight hum. The pickup is a Gretsch filtertron bridge pickup. How do I fix this problem?
Your wiring description is not all that clear.
I suggest you find a suitable wiring diagram (example here), and make sure your wiring matches.
I would then use a continuity tester to check your solder connections are good. You should also continuity check that you have not shorted your live connection to ground.
I found the issue was 2 different things, The first being as mentioned in a comment there was just a little bit too much solder connecting the volume knob, the second was I had no ground wire going to my input jack as the schematic I went off of didn't show one which seemed strange but I followed it.
She sings now though, and looks and sounds spectacular. Weeks of hard work on this project have been a success.