Electrical tape is slightly stretchy, insulating, fire resistant, vinyl adhesive tape used primarily to cover exposed electrical conductors, either to protect them from moisture or protect other equipment or people from coming into contact with them.
Electrical tape is generally applied by spinning the roll around the exposed wire in the direction that the tape comes off the roll. This applies some tension to the application as the adhesive pulls free from the roll, which keeps the tape tight as it is applied. This helps prevent any gaps from forming which moisture could enter or become a starting point for the tape to release over a period of time. Conversely, if too much tension is applied the tape will be stretched too far and the adhesive will loosen as the tape pulls back to a normalized state. The tension caused by the adhesive coming loose from the roll applies just the right amount to ensure a good wrap.
In general, you want to apply enough electrical tape to build up the application to the same thickness as the rest of the insulation on the wire. This helps ensure there is enough tape to insulate the level of voltage that will be on the wire (required insulation thickness increases with wire voltage, required wire diameter increases with the maximum current that can go through it). When taping the middle of a wire, it is a good idea to wrap up and then back again over your wraps. When taping the end of a wire, it becomes important to ensure a good, moisture tight seal. This is accomplished by twisting the tape into a one or two inch tail past the end of the wire, and then taping this tail back over the wire.
Most brands of electrical tape can be broken by hand when enough is applied. A quick jerk on the roll will stretch the end of the tape to its breaking point (slow pulls will just stretch it, loosening the adhesive). Other brands require a dispenser with a built-in cutter or the use of a knife or pair of scissors. There are two basic ways to complete the wrap, one for tape you intend to remove later and one for a more permanent application.
When applying tape you intend to remove later, fold the free end over itself to make a non-sticky "flag" at the end which will hang free off the rest of the tape. This makes it easy to find and grip the end of the tap to unwrap it, and prevents it from splitting down the middle. When applying tape for a more permanent application, give it just a little stretch as you lay it flat over the other wraps of tape (not too much, or it will pull loose).
Most electrical tape is black. This is a good, all-purpose color which doesn't indicate anything special about the wire it is applied to. Black is also the most resistant to ultraviolet radiation damage caused by outdoor applications which are exposed to direct sunlight. Other colors are available, and can be used to color code wires in special circumstances. Neutral wires, for example, must be white or light grey, and white electrical tape can be used to mark the ends of a non-white wire to indicate that it is a neutral (usually in the form of a continuous wrap a few inches long or three white stripes around the end). Likewise ground wires must be green or green with yellow stripes (or bare wire with no insulation at all), and green electrical tape can be used to mark non-green wire used as grounds. Other typical color applications are for labeling the phases on a three-phase system, marking the beginning of a wire in a conduit so the other end can be found at the other end of the conduit, or marking cables that need to be unhooked so they can be put back in the same place later.
Most professional electricians swear by 3M Scotch Super 33+ electrical tape. It's easy to break by hand, has just the right amount of stretch, sticks very well, and doesn't leave a gooey mess behind when it's removed. It's also one of the more expensive brands, but the extra price is often well worth it. Be sure to check the label to see if the electrical tape is appropriate for the conditions of your application. Tape is only guaranteed in a certain temperature range, up to a certain voltage, and for exposure to certain weather conditions.