I sleep very soundly. I didn't use to but I'm now pretty confident after all these years that the change in motion and other noises will wake me up if I drag. I try harder to find nicely protected and quiet anchorages than I used to. It's worth an extra hour's sail or motor for a quiet night. I do use a GPS anchor alarm occasionally if bottom, weather, and shore topography warrant.
Technique is important. I like to watch people anchor and it's amazing how many just let it go, throw some line in the water, and run back to the cockpit to get the drinks poured. Stopping the boat with the anchor is a particularly bad and common technique as it's hooked in reverse and then has to reset.
I bring the boat to a complete stop watching the shore or water along side. The anchor is let down as the bow blows off until it just touches. The chain is then let out very slowly so that it lays out neatly along the bottom as the bow blows downwind instead of landing in a heap on top of the anchor, possibly fouling it. When the chain is all on the bottom, I let out the rope rode keeping enough tension on it to keep the bow up. The boat blows downwind more or less broadside in most conditions by controlling the line tension.
When I have about 3/4 of the scope I plan to use, I snub the line on the cleat if the boat is blowing down fast. It's pretty obvious if the anchor takes a bite. In quieter conditions, I will pull the line up above the rail and give it several hard heaves. Often I can feel the anchor dig in with each pull. Sometimes, I can feel it skittering and clinking over cobblestone like bottom or ledge if I've picked a bad spot. I sometimes feel the kelp it hooked on pull loose at the roots. That usually means pulling it all the way up again, clearing it, and starting over.
Once I have a good set, I let out the full scope. If anchoring under power, I put the engine in reverse and run it up to about 2100 watching the shore for any signs of dragging.
Proper anchoring takes a while but I haven't dragged in the night since the early 80's.