To be able to search for the apartment that you really want, you first need to list all your 'musts'. For instance, does it have to be located in a convenient spot (ie. Near transport areas), do you want a studio type apartment, do you want amenities to be provided, do you want two rooms if in case you'll want a roommate later on, etc. Defining these things will help you narrow down your searches. Moreover, I think indicating the probable length of stay that you're planning to would matter. Or you could just talk to the landlord/lady about this. All the more important matter, which I almost forgot, is how much you can afford to pay. Personally, I consider this as the topmost filter whenever I move from one apartment to another. Then comes all the other features that I l'm looking for.
The next thing to do is to search the internet for reliable apartment-search websites in your area. Pretty sure there are a lot so you also need to do quite a few readings/reviews to see if these are legitimate sites.