Oracle Text

At the beginning of each opponent's upkeep, that player chooses draw step, main phase, or combat phase. The player skips each instance of the chosen step or phase this turn.

Card Rulings

12/1/2004 That opponent skips only the phases or steps that are chosen.
12/1/2004 If there are multiple phases with the same name in the turn, your opponent skips them all. This is true even if a new step or phase is added to the turn after the ability resolves.
12/1/2004 If more than one Fatespinner affects you at the start of your upkeep, you can choose the same step or phase for each one.