One of the best ways to let people know about your local apartment is by posting about it in local shops. While obviously we don't want you to go around sticking up fliers randomly, there is nothing wrong with asking local businesses if they don't mind having your advertisement somewhere that is visible. You may even want to think about ordering some cheap business cards with the address, your phone number, and a small picture of the building and asking if it would be okay to leave them there. You may offer to give your tenants something regarding that business. It may be a menu if it is a restaurant, or a gift card if the locations gives those out. Always be willing to work with the business owner. After all, they are giving you space in their area of income.
Another way that has been tried and true in regards to getting results is putting up signs. This can be something as simple as sticking a piece of paper to a telephone pole or a street light. If you print out the information for your available apartment and tape it up in different places around town, you are certain to get results. This is something that has been done for decades and hey, why mess with a winning system? Just one word of advice: remember to take down the advertisement once you have found a tenant so you don't keep getting those phone calls.
There are dozens of ways that you can get a tenant for little or no money. This is true whether you use the internet or not. After all, we survived before it existed so there's no reason you can't get a tenant without it.