Teleporters produce instantaneous, discontinuous transmission of particularized matter via instrumentality of the spatial continuum.
In other words, they make you stop being in one place and start being in another place.
Teleporters are held items with infinite usage. Pressing the action button while carrying one will cause you to teleport between 4 and 8 tiles horizontally in the direction that you are looking, or upwards if you are looking up. You cannot teleport downwards in the classic edition.
If the destination tile is a solid block, the teleporter tries to find an empty space up to 3 tiles above the selected location - If there is no viable space, the teleporter will warp you into a solid block and you will be killed.
Buying a teleporter is generally not recommended for the unprepared, as they are a quick path to death if you don't understand and accept the risks and limitations they have.
On another note, the Rare Item shops that stock Teleporters may also sell jetpacks which are far more effective for a slightly higher cost.
Teleporting in mid-air does not reduce momentum, so can not be used to evade fall damage. The only exception to this is if you teleport directly onto ground level. You shift from 'falling' to 'standing' states without landing, bypassing the damage.
Old vets of the Quake series rejoice! If you teleport into space occupied by an enemy, they will be rent asunder, regardless of toughness. The only enemies immune to telefragging are Olmec and The Ghost.
Note, however, that telefragging enemies does not count towards your kills. This means that killing a shopkeeper in this manner will not cause you to gain a wanted level.