Did you ever notice that on TV, the Survivor that somehow managed to erect a simple shelter in a howling rain the night before is magically in dry by morning? Does that match your camping experience? Not mine either. Wet clothes range somewhere between ‘miserable’ and ‘deadly’ depending on the weather. Fortunately, on my last hiking trip my friend Doc taught me a trick that helped me (and can help you) have dry clothes by morning.
What you need to dry your clothing
You do need a dry towel for best results. One of those super-absorbent camp towels works. Any dry material that’s more absorbent than your clothes will do, though. Remember the book Hitchiker’s Guide to the Galaxy (inspiration for Wikipedia) that had as its first rule “Always bring a towel”?
How to dry the clothes
First, wring the clothes as dry as possible by hand. Lay out the towel, then lay the wrung-out clothes on the towel.

Freshly hand-washed hiking pants and socks. They need to be dry by morning or Sad Hiker.
Roll towel and clothes up into one big jelly-roll structure.

Make a towel/wet clothes burrito, step on it awhile, then hang up the mostly-dry clothes for a bit.
Now step on it awhile. A lot of the water that was left in the clothing ends up on the towel. Unroll the lot and hang everything up to dry.
This method gave the outfit what felt a twelve-hour head start on drying and left my hiking pants (quick dry fabric) wearable after only an hour, and even my thick hiking socks perfectly dry after about eight hours in a regular room with neither breeze nor sun. For a hike in forty-five degree weather, this was the difference between comfort and potential hypothermia. Hypothermia is serious bad news (you can read about it here), and even if you don’t get too cold you can burn a Lot of extra calories trying to keep up body heat if you’re wet. It’s just a little trick, this fast-dry method; but a very useful one.
Bonus tip: Drying shoes
Wet shoes happen a lot when you’re doing a lot of walking off of the pavement. Wet feet are even worse than wet clothes, because you add a higher risk of blisters and foot infections to the problems of cold and discomfort. This helps: Stuff something absorbent tightly into the boots (especially the toes) overnight. Newspaper works pretty well.