How to play a planeswalker such as Sorin, Lord of Innistrad?
I know I add 1 loyalty counter at my upkeep.


huh? no. Outside of the effect of a spell or ability, you only add loyalty counters onto Sorin when you place it on the battlefield, and when you activate its +1 Loyalty ability.


  Can I play the -2 ability twice or only once per upkeep?


No, for two reasons.


You can't play it during your upkeep at all. Loyalty abilities can only be used "as a sorcery". (On your turn, in a main phase, when the stack is empty.)
You can only activate an ability of a given Planeswalker once per turn.



  My other question is can I play +1 and then -2 on the same upkeep?


No, for the same reasons.




  606.3. A player may activate a loyalty ability of a permanent he or she controls any time he or she has priority and the stack is empty during a main phase of his or her turn, but only if no player has previously activated a loyalty ability of that permanent that turn.