It’s best practice to wash your new towels before you use them, because the first wash will make them a little more absorbent (meaning they'll dry you more quickly).
After use, drape your towels over a bar or hook instead of folding them - the extra surface area exposed to air will mean that they dry more quickly, which is what you want. Bacteria thrive in warm, moist environments, so minimising dry time also minimises bacterial growth (so less chance of a musty towel).
Wash your towels every three days. Separate out your colours and wash like with like. Be mindful of the items you include in the wash, as zippers, hooks, and velcro can snag the loops, damaging the towel.
Begin by pretreating stains, then wash your towels in cool water on a delicate cycle. Avoid using fabric softeners as they build a film up over time that makes your towels less absorbent.
Before you put your towels in the dryer, shake each one out. It keeps them from twisting into a ball, reduces drying time, and helps stop wrinkling.