Clean your records well before playing. If I get a thrift-shop beauty, I'll give it a quick bath and then play the album while wet on a cheap turntable dedicated to this task.
After that, I'll wipe it dry, lube it up with some good ol' Gruve Glide, and settle back, transported to a slightly mildewey nirvana.
Love your tonearm. Use a bent tonearm, rather than the straights used for skratching. The S-shape will keep the cartridge aligned as it gets closer to the center of the disk, reducing stress that causes skipping. Balance your tonearm.
Buy a good-quality phono cartridge. I didn't know anything about cartridges, and was sold a decent, $25 Shure general-purpose thingie. Worked good! Had a lot of problems with skipping, and some of the highs were slightly distorted. Upgraded to a better cartridge, and the results were amazing.
Stay grounded. Ungrounded cables cause hum and static. Check cables regularly.
Keep your levels in the yellow. When your recording software starts clipping, nastiness results. Better to amplify the perceived volume in the software than get stuck with digital clipping.