What are the instructions for hand rail for stairs? How long should the rail be? How far above the stairs should the rail be?

Not quite that easy. There are a number of building codes in the US and your locale may have another one. As a general rule, top of the rail is 34" above the step at the nose of the step. However, finish of the rail depends on whether there is a landing at the top or bottom, an open doorway, how much floor before the sidewall ends. Best to check with your permitting department to see what code they use. Railings must return to the wall or contact the door frame wall so you can't catch a sleeve on the open end. If you Google "handrail installation" you will find various installs depending on floor layouts.

Between 30 and 34 inches, measured at the tread nosing. Rail cannot protrude into the stairway more than 3.5 inches. Some codes require that the end of the rail turn into the wall.