Don't be shy -- start with the obvious -- word-of-mouth. Ask friends or coworkers for ideas on where to look for an apartment. Professional resources include real estate agents or apartment-locating services. The usual charge for this service is the equivalent of one month's rent, which is paid by either you or your new landlord. Find out who is responsible, and get it in writing.
If you have time and tenacity, you can check the classified ads in your newspaper. But you'll save time and money, and rule out unacceptable apartments, if you keep in mind that some ads are just come-ons.
When you call about an ad, insist that the landlord define terms you don't understand and explain the flowery adjectives. For example, cute may mean tiny, and prestigious can be another word for expensive.