The tap should be straight up and down, more pointing to the rear of the engine.
Assuming it is a plastic type carburettor with the white primer cap, I would suggest cleaning out the area behind the white primer cap being careful not to lose the needle. in this part there is the brass jet (the screw that holds the primer on) the float (looks like a little white box with a hinge on the end, the needle (goes back in pointy side up) and a black O ring seal ($2 from any mower shop at the most).
A new spark plug is not always required but can help matters, they simply screw out, put the new one in and put the spark plug lead back on. The air filter could also do with replacing once a year, thats at the top of the handle under a black plastic cap.
The easiest way I find to start them is, turn the fuel on and wait for a few seconds, push the primer button half a dozen times (if you cannot hear a very faint ticking noise when the primer bulb is pressed it is not priming and you need to clean that area I was talking about back at the start) put it straight onto run and pull the rope.
If the fuel has been left on in the past it will flood making it very hard to start, to unflood it, remove the spark plug, with the fuel turned off pull the rope a dozen times, dry the spark plug and refit.
