The drain method is the most classic: You simply pour the pot of pasta and water through a colander set in your sink. If you are interested in keeping some of the pasta water, place your colander over a bowl. A major drawback for some people is carrying a hot pot of water from stove to sink. An advantage is that the colander is a superb multitasker and most kitchens will already have one on hand.
The spoon-shaped claw has spiked teeth along the rim to grab and hold pasta and a perforated center to allow water to drain away. It works best with long strand-styles of pasta such as angel hair, spaghetti and fettuccine: Medium shapes tend to get impaled on the teeth and small shapes drain out with the water. It is also used for serving pasta, so it's not quite a uni-tasker.
The scoop is a long handled colander with a wide flat base that's designed to scoop the pasta up out of the pot. It comes in handy if you want to keep the hot pasta water for another use or if you don't want to haul a pot of hot water across your kitchen to drain in the sink. It works best with shaped pasta, but can accommodate strands of pasta as well. The scoop also works for blanching vegetables and scooping beans.