A Realtor generally knows the landlords in the area where they work and can lead you in the right direction. If you can not afford a Realtor, local print media, word of mouth, sometimes church bulletins have apartments listed in them. Super market bulletin boards sometimes have apartment listings.
Your credit rating will be important, and be sure to ask lots of questions about the running of the property before accepting an apartment. If you do not smoke make sure the owner does not smoke, etc. Good luck in your endeavors.