The easiest way to find an apartment to rent is through a real estate broker. Talk to one and explain the type of apartment you're looking for. However, when working with a real estate broker, you have to realize that they need to convince you to rent the apartment. That's how they make money. To make sure that you don't get ripped off, do your own research about the building and the locality to make sure that you know what you're walking into.
The internet is your number one friend and the one place that you'll find hundreds of apartments to rent without having to deal with a third party like a broker. Websites like Craigslist are a great place to find apartments. However, you do have to be careful of spam.