As picturesque and lovely as it may be, Zurich is tough for travelers on lower budgets. This is definitely a business city with an emphasis on the banking crowd so most everything is geared toward those on liberal expense accounts.
There are a few hostels in Zurich, and even though they are quite pricey at least they keep the city within reach of the backpacker set, for a night or two at least. Hotels in Zurich are notoriously expensive as well, with prices rivaling those in Stockholm and Oslo.
Once you have a bed things can get a little better, as transportation can be affordable, especially by just walking or using the free bikes offered during summer. Most of the attractions are reasonably priced as well.
Food can be tricky as most of the proper sit-down restaurants will charge outrageous prices. There are many street stands selling sausages and such, so at least filling and affordable meals aren’t completely out of reach. Drinks are quite expensive as well, so you might think about bringing something along with you.