If you are familiar with the area and its neighborhoods, that gives you a distinct advantage for your apartment search. If, however, you are relocating to a new city or are not particularly knowledgeable about the city, you may want to contact an Apartment Locator or an Apartment Finder.
Once you have located your "dream apartment", or as close to your perfect apartment as possible, now it is necessary to pay extremely close attention to the particulars of the rental agreement. An Apartment Lease is a contract between you and the landlord. Once agreed upon and signed by the tenant and the landlord, the rental lease creates obligations and restrictions for both parties. The most obvious covenants of the apartment lease are the length of the rental, (Six month lease, one year lease, two year lease, etc.) The amount of the security deposit, when the rent is due, who is responsible for what utilities. Also in that apartment lease, however, are stipulations, (sometimes in small print) that can cover a great variety of landlord and tenant obligations and restrictions.
If you do not understand every single clause of that apartment lease then do not sign it until you do understand it. If necessary and if possible, request assistance in interpreting the lease from a trusted source such as a knowledgeable friend or family member or employer or professional, or anyone else who can understand it and explain it to you. If necessary get legal advice. It can cost additional funds if you do not qualify for free legal assistance, but that additional cost might save you a ton of money and save you a ton of heartache and aggravation down the road.