1. Find a suitable anchorage spot, especially if anchoring overnight.
Ideally, you want an anchorage that is protected from the wind in all directions. Make sure there's sufficient depth of water, even at low tide. 13 feet of water at high tide may mean you're in the mud at low tide. Remember, your boat is going to swing thanks to current and wind, so make sure you have enough swinging room in relation to the amount of rode you have out. Finally, avoid areas where the bottom is awash with debris such as stumps, boulders, etc. Admittedly, this is often hard to tell, but sometimes the shore reveals some good clues.
2. Once you've found an anchoring spot, move slowly towards it into the direction of the wind or the current. This article assumes you're releasing your anchor from the bow of your boat (the front) and not the stern. The anchor should always be released from the bow!
3. When you reach your anchoring spot, place the engine into neutral and slowly release the anchor overboard. The classic image we all remember of the skipper throwing the anchor carelessly into the water is asking for tangled line/rode. When the anchor reaches the bottom, place the engine into reverse, slowly backup, and gradually let out your rode until you have a scope of 5:1 or more (ideally 7:1). This means that if you're anchoring in 20 feet of water, you need 100 feet of rode released).
When you feel the anchor "grab" (i.e. the boat will no longer move back) the anchor is set. When the anchor is set, "back down on the anchor" or give the engine some throttle in reverse to really dig the anchor into the ground. Be careful not to give it so much throttle as to unset it.
Don't get frustrated if it takes you a few tries to set the anchor. Some anchoring bottoms are a pain to anchor in, but normally your persistence will be rewarded.
4. Make sure the anchor really is set. Take a couple of bearings on land and watch them to make sure the anchor is not dragging. Monitor these bearings for at least the first 30 minutes after anchoring. If you have a GPS, use the "anchor drag" utility to alert you incase your anchor does start to drag during the night. Don't use your GPS in the first 30 minutes after anchoring! GPS' have a margin of error of 30 or more feet. You could easily be drifting into another boat before your GPS alerts you.
5. To release the anchor, pull the rode in until the rode leads vertically into the anchor. Tug on the anchor and it should release. Now you have the fun of bringing the thing in.
Here's also one of the more helpful videos for those who prefer to learn this way (skip to the 35 second mark to avoid the ads):