There are plenty of tutorials for cast iron care across the internet, I'm not going to re-invent the wheel here. I had a great system for caring for my cast iron pans, and they have lasted me for years, and will likely get passed onto my kids.
But when switching away from paper towels, I had a few hiccups in my system. I used to wipe the vegetable oil onto my cast iron with a paper towel, and though it gave me lint issues, it was how I was taught and I didn't know a better way. I tried to delegate one washcloth to being soaked in oil, but it got black and I put it in the pile with the dirty towels to get washed. Then before it got washed, I needed to season my pan again, and I ended up with three different cloths that were saturated in oil and nothing would clean it out. Worse, they had mingled with the rest of the towels and I have a bunch of towels that still don't absorb very well due to the grease content. (Cleaning those is a project for Future Heather.)
Insert some brilliant soul on the internet and a light bulb in my brain.
I now keep a small jar on the counter with 1/4 inch of vegetable oil and a dedicated pastry brush (not a silicone one, an actual bristle brush). Any time I heat a pan up, I brush on a thin layer of oil to melt into the pores, and it keeps my pans nicely seasoned. I can also make a point to concentrate on problem spots, as needed. Because it's so easy, deep-TLC days are fewer and farther between, which is also nice.
The best part? I have one pan that I keep less seasoned, so I can leach extra iron out of it as I am prone to iron-deficient anemia. This is the pan that I use for acidic foods and things that will require scrubbing no matter the seasoning level. This brush-on seasoning process actually helps me keep this pan at a minimum level of seasoning, so I can get maximum iron leaching without letting the pan get TOO abused. I call that a win!