They're called phrasal verbs and I'm afraid there's not one rule as to when you need to add 'up'.
Sometimes 'up' is an intensifier ('screw up'), sometimes indicates a completion ('eat up'). Sometimes it refers to a movement? (I am thinking of 'stand up', that differs from 'to stand' because the first refers to the action going from a sitting point to that of standing, while 'to stand' is just standing still on two feet.)
Of course these are just examples and it may not always be the case. Phrasal Verbs are something you will have to learn to use according to each situation.