First you put in your search terms on the left hand side of the page. You can choose everything from the number of bathrooms (something I wish Craigslist would add) to the type of home you're looking for. The results pop up in the area below the map.
Instead of clicking on each listing like you would on Criagslist, Zillow gives you an quick view of each apartment showing basics like how many beds/baths, the rent price, and the type of property. You can also hover over the thumbnails to see a larger version of the pictures included with that listing. All this without ever having to leave the search results page!
Once you find a listing you like, it pops up with basic information. First there's the overview which includes pictures and info on the apartment.
Now here's where Zillow really excels. Not only do you get basic information about the apartment, but they also offer pictures of the neighborhood and demographics about the area! Since we're doing a long distance move and aren't super familiar with all the different areas of Chicago, it was extremely helpful to be able to look at the neighborhood demographics. Now we know that Lakeview is mostly 20 and 30-something people with no kids. Works for us!
Already, I'm in love with the apartment we found above. It's in Lakeview which seems like a nice area based on the demographics and the photos. As an added bonus, the apartment's eerily similar to our current place: it has a spiral staircase leading up to the attic master bedroom...we'd feel right at home :)