So far this season I've only been able to set about 20 traps on two farms. But I've only caught a skunk and fox. What should I do to get out of my 3 week not catching anything period?

Try different locations on those farms. Sometimes moving sets around will surprise ya. Are ya using long distance call lure near sets? If not that should increase your catch. A different lure may help?

I get into huge slumps as well trapping on public land. I don't know what to do either.

What animals are there and how many.
If you are making the proper species specific sets for your area you should be catching the animals IF they are there.

Seems like right after deer hunting season every thing slows way down for me as well. This year I expanded and just found a few more places to trap and spent the day scouting and making a few new sets. Hope my luck changes soon but nice to see some new territory.

I’ve been on a dry spell for coyotes too. Been catching lots of fox, but no coyotes. I think the density here is just lower than I’m used to.

I am using a long-distance lure and use multiple baits throughout the farms. My problem might be my sets. I'm still learning where to set them. But it also could be less of those animals are around me. I am trying to target fox and coyote.

After deer season here bait is hit or miss for me. Probably lots of gut piles and road kills around, who knows. But I do have good luck with sets using urine or gland lures. Post and flat sets, mix it up. Lot of territorial sets seem to work better this time of year for me. Bait gets interesting again later in December than right after deer season here.
I also do better with different species odors...fox, beaver, mink, seem to be more interesting to coyotes for some reason.

Is the prevailing breeze right? Try setting on the other side of the fields or roads

basic locations are - along any woods/farm roads - any place a road comes into a field - corners of a field that meet woods or another field - where a field or woods meets a waterway - along fencerows near any of above - any dump or scrap piles that stand out in a field. Also LD call needs to be up wind from sets - a compass will always tell ya NW or W direction in case you're not sure. Good luck !