I, too, arrived about 3 weeks ago. I visited close to 15 apartments my first week - and had appointments for 30 more in the following weeks. My husband and I were lucky enough to have a woman at a service help find stuff for us, but we had to do a lot of legwork as well.
We were very lucky and got the first apartment we applied for.
My advice:
1. Get all of your paperwork in order. This means your proof of being debt-free from the kreis bureau. It means showing that you have enough money for the security deposit or Swiss Caution insurance ready.
2. Visit a billion apartments. At open houses, be there early. We ran into a couple d#%!&bags along the way who wouldn't even let us in - because we were 15 minutes into a 30 minute visit window.
3. Don't get frustrated.
4. If you are even REMOTELY interested in an apartment, apply for it. Do not snail mail. Fax immediately over the forms.
5. It helps to bring someone with you who is a Swiss native. It certainly helped us with explanations, translations, and small talk.
6. Be friendly with the current tenant. I swear this was the one step that got us our new place. He really clicked with my husband and I, and told the private owner of the building that we'd be wonderful tenants and that we "really understood Switzerland" or something to that effect.
7. Be aware that some places are more popular than others. Branch out from Kreis 1, 5, 7 and 8... and sometimes Kreis 2. When we visited places in Kreis 5, there were hundreds of other people visiting. If it was a new place, there were hundreds of people visiting. If you visit an older apartment in Wollishofen or Wiedekon or wherever... you've got a better chance because there might be only 30 applicants as opposed to 300. The odds are better!
You'll find a place. It just might take some legwork and some friendly banter. I cannot wait to move into our new place. It's not my dream home, but it is home!