1. Post Locally. Posting about an apartment in local businesses can really help out someone who is looking. You can always just ask someone if you can place some fliers or business cards in their work place. You may even help them out in turn by purchasing a small gift card for your future resident to their business location.
2. Put It Online. There are dozens of sites where you can post for free about different things. Sites like Craigslist are always popular for people to look for new housing arrangements and you can be certain that people are going to see your listing as long as you post it correctly. Posting it online also helps to bring it to more people as they do not have to be in the area when they look at your apartment online. I have been looking at certain apartments a few states away for friends and it is so wonderfully easy.
3. Word of Mouth. While this technique isn't used as much anymore, it has likely gotten me my next apartment. I mentioned to a friend that I was looking to move and they put me in touch with someone who had an empty apartment. You never know how useful your friends can be in helping you out when it comes to filling your rental property, so put some feelers out there for those who may need somewhere new.
These are three of the most obvious ways to try and get some new residents without paying an arm and a leg, but sometimes there is nothing wrong with trying the obvious ways first. In fact, they are well used for a reason. Let us know what other methods you have used and stick around for some more ideas.