Most anglers will fish with the bait sitting still when they go carp fishing. Some anglers do drift, but for the most part, the better carp anglers usually will be fishing with their bait sitting still.
Bottom fishing is the most popular way to fish for carp. Cast your bait out in a good spot and let it sit on the bottom until you get a bite or until you change spots.
Fishing with Bobbers or Floats
Using a float or bobber is another way to target carp when they are suspended up in the water column, however, you will usually have more success by fishing on the bottom.
You can drift for carp as well. Some anglers do this in a river or when fishing on a lake with a light wind. It can be effective, but most anglers usually report better success by finding a good spot and letting the bait rest on the bottom.