Plastic expansion anchors: some of the more commonly used. The larger the anchor, the more weight it can hold. And these can be installed in metal, wood, even concrete. When the screw is put in place, the plastic expands, gripping it to the material. However, they aren't nearly as strong in drywall, because they don't have anything to expand into. Just predrill a hole just large enough for the anchor, tap in with a hammer, and insert screw.
Threaded drywall anchors: Are popular because fewer tools are needed. Just a Phillips screwdriver, and like a screw, thread it into place, until the head is flat against the surface. Follow that with the screw included with the anchor.
Winged Plastic Anchors: Offer more strengh in drywall, because wings brace against surface inside the wall. Predrill a hole large enough for the anchor and press in until head is flat against the surface. Included with the anchors should be a special tool. Push tool into opening until wings pop out. If you don't do this, the anchor will not hold. Follow that with the screw.
Hollow Wall Anchors: Much stronger than plastic anchors, with metal wings that brace against the surface. Most are installed by hammer, but it's recommended you pre-drill, first. Tap into place, and screw into place. As you do this, the sleeve of the anchor is pulled back, bracing against drywall.
Toggle bolts have spring-loaded metal wings that close for insertion then spread out flat on the backside of the wallboard to create a sturdy, wide anchoring base for moderately heavy loads. Toggle bolts are good wall anchor choices for large, heavy pictures, wood shelves, and glass items like candle holders or sconces with glass globes. To install toggle bolts, drill a hole just large enough for the closed toggle to go through. Remove the bolt from the wings and place a bracket or other hanging fixture onto the bolt. Screw the bolt back onto the toggle wings. Gently push the closed wings through the drilled hole in the wall. The wings spring open on the backside of the wall when they push all the way through. Tighten the bolt and fixture.