I am moving into a new apartment, that is rather run down, and the landlord doesn't care what I do to fix the place up. The old gas stove is shot, and I've always been partial to electric, glass tops. I can get an incredible deal on one, and would like to cap the gas line, and install the electric. Im a pretty decent jack of all trades, and have added circuits, but I don't have a clue how to add this outlet where one does not exist

240 volts is nothing to mess with. If you "don't have a clue ", maybe you shouldn't. Basics are a breaker box capable of handling the increased load, appropriate wire and breaker, 4 prong outlet, drilling the walls and floor as appropriate and your time. Make sure the house wiring can take the load, at least 30 amps. If the place is run down, as you say, wiring may not be up to code as it is.

All you do is to get a double breaker for the breaker box at the min. ampacity rating, at least. You could need a 30, 40, or 50 amp breaker depending on the name plate on range. Then you size the wire for the range. The size wire depends on amperage and distance. Normally, I would use 6-3 copper with ground. A 240 volt line is only two 120 volt lines. You will wire the red and black to the breaker and the hot legs (brass screws) on the receptacle, white goes to neutral (silver screws) and ground goes to green. On the pig tail you can get 3 or 4 wire plugs to match the receptacle. Since you are using a 4-wire plug, you will remove a jumper that ties neutral and ground together. Then ground will go to cabinet and white to neutral. It's very easy.