To hang pictures or other objects on walls made of sheet rock you'll have to use wall anchors. This is because sheet rock is made by compressing plaster with fibrous materials, such as fiberglass or paper, and as such, it does not have the density to support nails or screws. If you can't find a stud, or the placement of the stud isn't optimal, using wall anchors is your best bet, and they are quite easy to install. You want to make sure you use the proper type of wall anchor for the weight you need to support. Plastic anchors are the weakest of those available, and they should only be used for lighter objects, with a maximum of 10 lbs. Threaded drywall anchors can hold somewhat more, up to 20 to 25 lbs. There are others, but these two are the most commonly used.
Step 1 - Drilling a Hole
The first thing you need to do before you can install the wall mount is drill the hole where it will be. Wall mounts work by spreading the pressure out of whatever is hanging from them across a larger area of the wall, so they need a larger hole to fit through. If you are using a simple plastic wall mount, use a drill bit that is about the same diameter as the wall mount itself. If you are using a threaded drywall anchor, you will need to make the hole a bit less than the anchor. It is best if you make the hole about the same size as the end point of the anchor so that the threading can catch completely in the wall.
Step 2 - Installing the Anchor
Once you have the holes drilled, and if you have a plastic anchor, install it into the wall by tapping on it gently with the hammer. Be careful not to tap too hard and force it in; the plastic can buckle under the force if too much is applied. If you are using a threaded drywall anchor, screw it into the hole you drilled until it is firmly screwed in. It is natural for the area of the wall surrounding the anchor to crack or become distorted; it will smooth out as the anchor is screwed all the way in.
Step 3 - Putting in the Screws
Once you have anchor securely installed in the wall, you can screw in the screws that were included with the kit. If you're using a threaded anchor, the points will get pushed out of the other side. These don't serve any support purpose and can be removed, if you're so inclined, but it's not necessary. Now, your wall anchors are ready to accept wall hangings.