What card should I play when my partner has bid nil and I can't follow suit but do have Spades?
It depends. Have you and the opponents bid for most or all of the tricks? If so then your left hand opponent (LHO) will probably not let the trick go by for fear of going down themselves. If not, and RHO has led a low card, then partner's nil may be in danger and you probably won't have to work hard to get your bid, so you need to protect partner from LHO playing low.

If you are going to protect partner, do you think he will have to follow suit? If so, then you can either trump small so he can throw a high card, or discard small and save your strength for later if you think he can duck this trick. If not, then a high trump will allow him to under-trump if he has an awkward middling trump. 

Of course, if you know the cards that have been played, hopefully you'll know how many high cards are gone and what risk this trick poses. A good partner will also try to help you by good discarding - ideally he'll discard short suits first (if you have K765432, you don't gain anything by chucking the King early!), and by discarding a low card in a suit he's essentially saying "this suit is safe, please lead it whenever you can". Deliberately winning the lead with the intention of giving partner a free discard is very helpful.

(In any case, aren't spades always trumps? Or is that just the MS online version?)