This is the method I use:
1. Heave to.
2. Drop the anchor off the windward side of the stern beside the cockpit. I store my 250 feet of anchor rode in a random heap in my stern locker in a laundry basket, along with the anchor and chain.
3. As soon as the 25 feet of anchor chain passes over the side, I pass the (fiber) rode through a snatch block.
4. I haul the anchor rode to the bow. A hauling line attaches to the snatch block that runs up to a bow skein chock (inboard of the shrouds), through the chock and back to the the snatch block (outboard of the shrouds) at the stern, in a loop.
5. I let out the appropriate length of rode, and then snub it off on the jibsheet horn cleat (at the stern).
6. The forward/downwind motion of the hove to boat (the motion is about 1 unit downwind for every 2 units forward) sets the anchor.
I’ve anchored without need of an engine and without ever leaving my seat in the cockpit.
1. Raise the jib. Haul it to windward so it’s taken aback. (If the wind has picked up since anchoring, I left out more rode first to create a better catenary angle.)
2. Raise the main with the mainsheet let all the way out till the main begins to luff. Set the tiller to steer fully upwind. Tie it off.
3. Wrap the anchor rode around the jibsheet winch and haul the boat toward the anchor.
4. When the anchor unsets, I quickly haul some more line up by hand. (The boat is now underway, hove to.) Once unset, the only tension on the rode is from the weight of the anchor and rode/chain.
5. With the snatch block loop, I haul the rode back to the stern beside the cockpit.
6. Snub off the rode when the anchor is safely off the bottom.
7. Release the windward jibsheet and take in the lee jib sheet. Set the rudder. Set the mainsheet. (If I intend to get underway from being hove to.)
8. Haul in the anchor rode till the fiber rode-to-chain attachment is above the water line. (Dragging the anchor and chain through the water while underway usually removes most of the bottom mud.)
9. Take the rode out of the snatch block.
10. Haul the chain and anchor aboard by hand. Store the anchor and chain in the stern locker (where the sinky bottom mud never gets inside my cabin's air space).
I have now taken in the anchor and gotten underway without leaving the cockpit and without need of an engine.
If you can't perform all important operations without an engine, you don't have a sailboat. Instead, it's a wind-assisted power boat. I learned to sail in Sweden, where only lubberly wimps were dependent on an engine. I'm amazed at how few skippers here in the US don't even know how to take in their main without powering into the wind. Good luck if your engine doesn't start! Heave to instead. Here's how I do that (single handed):