Making your environment less 'hummy'. The kind of hum that pickups pick up is caused by electromagnetic fields in the environment; if you can identify a particular item that is causing the hum, then you may be able to turn it off or move away from it. Items that can cause hum include mains transformers, motors, and, as Tetsujin mentions, old style CRT screens.
Try to get your instrument not to 'catch the hum' so much. You might orient a radio antenna to catch more signal; conversely, you can often reduce hum significantly by turning the instrument around and finding the least noisy position.
Don't 'hum' yourself! If you've experienced hum getting worse as you are near the instrument, this is because your body (being mostly water) can pick up and retransmit hum from the environment. You can reduce this effect by grounding your body - often people notice this when they touch the strings or bridge of the guitar, but you could also try using a grounding wrist strap (https://en.wikipedia.org/wiki/Antistatic_wrist_strap). OK, arguably not a cool look and might not work with all playing styles, but it can help when recording! Of course please follow all relevant safety instructions - don't clip it to the nearest live wire.
Shielding the instrument - you can reduce the amount of hum the instrument picks up by surrounding (as much as possible) the pickups and electronics in a conductive foil, tape, or paint, usually applied to the inside of the pickup and control cavities, and back of the pickguard. To work best, this shielding needs to be continuous and have a good connection to earth. Although it's said not to be the best thing, I've had pretty good results with kitchen foil just crimped on to the earth wire.
Checking your wiring : make sure all the solders and connections to ground are good; make sure you have shielded cable for any non-earth connections inside the guitar (the shield would itself be connected to earth). Metal hardware on the guitar should be grounded via the bridge - check the bridge is grounded.
Battery - on an active instrument, check that the battery isn't running out of juice - this can make the electronics behave worse.
Cable - check that you are using an undamaged shielded instrument cable.
Changing your electronics - ultimately if you like the playability of the instrument but it's just too noisy, you could consider changing your pickups and associated electronics.