A very simple trick is to wipe excess glue off the outside of the applicator before screwing the lid back on. Use a dry paper towel or scrap of paper or fabric, but be careful not to glue the wipe to your fingers.
Using a wet towel can set the glue very quickly (so you can see excess glue and scrape it off), but if the moisture gets into the applicator, your glue sets there as well and clogges up immediately.
I had several tubes of superglue glued shut by a tiny drop at the very tip. Just wiping the tip off helped a lot, but sometimes wet glue gets into the lid before I wipe it off. Then I wrap a piece of paper towel around a tooth pick and wipe the inside of the lid as well.
Keep the glue stored with the lid facing up.