On the big field where runners can lead off, the basics for legal pitching with runners on base are:

Windup position:  Pitcher is on the rubber, hands in front of the body facing the plate.  Free foot (stride foot, opposite of pivot foot) may be on or behind the rubber.  From the windup, the pitcher may start his pitching motion and pitch; or, step directly toward a base to make or feint a throw; or, step off.  (Step off means stepping backwards, toward second with the PIVOT foot as the first move.) 

As soon as the pitcher steps off, he is an infielder and there are no restrictions on what he can do (except that he cannot make a motion that fakes making a pitch). 

As soon as he starts his pitching motion (usually by moving his free foot to take a rocker step), he is committed to make a pitch - stopping or throwing to a base is a balk. 

To throw to a base from the rubber, the first move must be a step toward the base.  (There may be some minor other movement to position the feet to make the throw, but usually a throw to a base will be clearly different from the start of the pitching motion.  If the initial motion looks the same as the motion on a pitch, it is a balk.)

The above is the wind up only.

Set position:  The pitcher takes the rubber with the hands separated, pitching arm at the side.  The pivot foot is in contact with the rubber, the free foot is in front of the rubber (meaning toward home, within the ends of the rubber), and the pitchers body basically is facing toward third.  The ball may be in the glove or in the hand.  Signs are to be taken from the rubber.  The pitcher should therefore take the rubber, hands apart, then look for signs. 

The pitcher may at any time throw to a base or feint to a base other than first, or he may step off.  For a throw or a feint from the rubber the pitcher must step toward the base.  Failure to step for a feint or throw is a balk.

Before pitching the pitcher must come "set".  This means hands together holding the ball in front of the body.  There must be a "stop", meaning no movement of the hands or body.  This "set" signifies that the pitcher now is ready to pitch, and from that position he may throw a pitch, throw or feint to a base (as above) or step off.  Once set, any movement (other than the head) not part of the a throw/feint/step off is a balk.  (For instance, turning the shoulders to look at first is a balk; coming set and then coming set a second time is a balk; taking a rocker step after coming set is a balk.)  If the pitcher does not come to a stop and pitches it is a balk.

Pick off moves:  A pitcher while in contact with the rubber may throw to any base, at any time before or after the set, provided he makes a continuous move to make the throw and he steps toward the base.  A "snap" throw without a step is a balk.  A right hander picking up the free leg toward third as though pitching and then turning and stepping and throwing to first has balked (a left hander has balked if his free foot is picked up toward first and goes behind the plane of the back of the rubber before throwing to first, or if he starts toward home and then changes direction back to first).

A pitcher in contact with the rubber MUST throw to first, but may feint to second or third (provided that the base is occupied or that a runner is advancing toward that base - a throw or feint to an unoccupied base is a balk).  A feint from the rubber must include a step toward the base.

These restrictions do not apply if the first move is the step off.  If the pivot foot is lifted and placed on the ground behind the rubber, the pitcher is not longer a pitcher but is an infielder who may throw or not throw in whatever manner he likes.  The only thing a pitcher who has stepped off may not do is make a motion that simulates his pitching motion.  (If the pitcher after stepping off throws the ball away, the base award is two bases, as it would be if an infielder threw the ball away.  One base is the award for a throw from the rubber going out of play.)