Q: What is the safest, simplest, and most effective method to anchor an average-size sailboat?

There is technique (and many strong feelings) to anchoring, but I don't think there are any great secrets beyond what is taught in sailing classes. Just practice and patience and a lot of small things.

Usually anchoring can be done simply and without drama -- the need for experience comes when things go wrong. (Like pretty much 95% of things in sailing.) Of course it's a lot easier to anchor a Rhodes 19 in a nice lake with friends you sail with every weekend, versus anchoring an unfamiliar Beneteau 50 you just chartered off an unfamiliar island with inexperienced crew you are sailing with for the first time.

The way to be safe is to practice adequately, build up experience, and to keep learning from other sailors. US Sailing and ASA both teach "Basic Coastal Cruising" classes that including anchoring, and many sailors are flattered to help others learn this kind of thing. NauticEd (http://www.nauticed.org/sailingcourses/view/anchoring-a-sailboat) also has a $17 online course that is probably not bad.

Here are some general tips that they would teach you in a class:

1. Pick an appropriate anchorage, based on (a) shelter from wind and waves and lee shores (b) good holding ground [generally mud or sand will be preferred] (c) adequate scope, swing room, and depth under the boat.
2. Coordinate and practice with the crew. Arrange hand signals if necessary. Do not raise your voice. Speak in complete sentences. Use headsets if helpful.
3. Use an appropriate anchor. There are many strong feelings on this. For muddy or sandy bottoms, a lightweight-type (Danforth) anchor, appropriately sized to the boat, is generally fine. Of course there are many fancy anchors now available (Rocna, etc.) that are fine too.
4. Use appropriate rode. In the Caribbean, all-chain rode (with nylon snubber) is typically used because coral reefs can chafe nylon rode, and all-chain rode typically requires less scope. If using an all-nylon rode, allow 7:1 scope for overnight anchoring.
5. Consult a coast pilot (or cruising guide or similar publication) and nautical charts for information and warnings about the anchorage. In the BVI, the aerial photographs in "Virgin Anchorages" are very helpful for the first-time visitor to unfamiliar islands.
6. Realize that the difficulty varies based on the conditions and the time of day. Anchoring in pleasant weather in a familiar spot with the sun up is one thing. An unfamiliar anchorage at night in a gale with cold rain or spray and a slippery deck is different and calls for much more caution.
7. Cruise through the anchorage once before picking a spot to anchor. Don't just anchor in the first place that looks good. If there are other vessels already anchored, they have the right to set the anchoring method in use -- single bow anchor, Bahamian moor, two anchors off bow, etc. They have the right to ask you to move if you anchor too close. Feel free to slow down and ask the other vessels how much scope they have let out, etc.
8. When you do pick a spot, allocate appropriate swing room for changes in wind and tide. Confirm appropriate depth with your depth sounder and charts.
9. Assuming you are anchoring with a single anchor off the bow (the most common method): As helmsman, point the vessel into the wind and wait until ALL headway has stopped. Instruct the crew to begin LOWERING (not dropping or throwing) the anchor. Hopefully you have a working motorized windlass and have marked every 10 feet of the rode with little indicators -- these are both great conveniences.
10. For all-chain rode, I like to first pay out 3:1 scope, then back down on it with the engine at 2,200 RPM. Then I pay out to 5:1 scope. For nylon rode, I generally pay out 5:1 rode, then back down on it, then pay out to 7:1 scope.
11. With practice, you can confirm that the anchor has set by looking at how the rode "skips" across the surface of the water when it gets tensed up. In any event, don't leave the boat right away after anchoring. Confirm that you are not dragging. One classical technique is to sight a pair of objects off the beam and confirm that they retain their alignment (i.e. that the wind isn't pushing you back). Of course there are now GPS alarms for this kind of thing.
12. If the water is clear and warm enough, DIVE the anchor to confirm it has set. Sailors in the BVI swear by this. The corollary is that you should plan to arrive in the anchorage before the sun gets low in the sky, so you can still see the coral heads and the ground and your anchor.
13. If the anchor doesn't set, the first response should be to pay out more rode and see if it eventually sets. If that doesn't work, just pull it up, circle around, and do it again. Speak in complete sentences to the crew and explain that you are going to do it over again. Don't get angry if it doesn't work -- there's no shame in repeating the process 2 or 3 times. You'd much rather get it right than wake up with a "bump in the night" at 2 a.m.! If you still can't get it to set, you may have bad holding ground and have to pick a different spot.
14. Sometimes, in a crowded anchorage, when you are trying to do this, the proprietors of nearby vessels will come out on deck and look at you with the death stare. And they will bring their fenders out and tie them on. In a truly obnoxious anchorage, they will even talk loudly about the "amateur" or the "credit card captain" in their midst. These people are dicks and you can't let them get to you, but the way to be a responsible citizen is to (a) know your own capabilities and those of your vessel [i.e. practice maneuvering when you are out in the open!], (b) don't attempt anything unsafe or beyond your ability (c) don't hit anybody (d) keep your calm with the crew. No jumping around, no yelling, no waving your arms angrily. Speak in complete sentences.
15. If a nearby, previously-anchored vessel says you are too close and you have to move, you have to move. If they just give you the death stare and the full complement of fenders, consider yourself warmly welcomed. Dinghying over with treats and/or drinks can be a good way to introduce yourself.