Be Professional Yet Excited. When you are showing off your apartment to a prospective tenant, you need to remember that you are selling something. You wouldn't work at a department store or a used car lot and be completely uninterested whether or not someone buys something. The same applies with your rental property. You are trying to sell your space above all others that this person has seen or will see. While we don't suggest jumping around like you've just won the lottery, you should at least appear to be excited about renting out the apartment. People will specifically look at whether or not you seem happy when you walk into the area and will base much of their feeling about the apartment upon your reactions to it. Be sure to keep their interest up with your energy.
Upkeep and Maintenance. I recently went searching for a new apartment and can tell you that this certainly needs to be mentioned. Keeping your building looking good and being structurally sound is something that should be common sense but sadly is not always. For example, one apartment I looked at was on the fourth floor of a building and had a hole in the floor of the bedroom. Things like this are not acceptable to most tenants, especially if you are trying to charge the same amount as other apartments. Having good curb appeal can go a long way as well, so make sure to keep the grass cut and maybe plant some flowers. You should certainly make sure that there are no holes or exposed wiring in your apartment.
These are two very simple ways to get someone interested in your rental property. While they may seem basic, you would be amazed at how many times we hear experiences that speak to the opposite of these ideals. Always exercise common sense when looking for a new tenant.