Depends on the conditions. In calm seas I will pull the rode (rope) in by hand until the boat is over the anchor, then use the windlass to bring the chain and anchor up (50 feet of chain, 40 pound Danforth, 20 pound kellet). In the few times wind/current pressure was strong enough that I could not pay in by hand (boat displaces 35,000 pounds) I used the windlass, but in short cycles so as to not overload the motor. In either case the main engine is running and if necessary I will put the engine in gear while at idle to help take some of the pressure off of the windlass where conditions dictate.
There have been a number of times when we experienced a strong blow during the night while at anchor. In the morning when seas were calm, getting the anchor unstuck from the bottom can become quite the chore. Wind pressure causes the Danforth to set deeper and in those times I have to work the windlass in short cycles to gradually unseat the anchor so as to avoid popping the breaker. I will work the Maxwell windlass to the point of almost a stop, then release the foot switch. Then repeat until the anchor is free.
Other times the anchor will hang up on something; log, tree, rock, etc. In those rare cases I will motor the boat in the opposing direction and then back away, which causes the anchor to unseat from whatever it was stuck on. So far these techniques have worked over the years and have yet to end up cutting away the ground tackle.