Great info above; a few things I like to do below:
I like to give a basic instructional tasks to 'weed the garden', especially when there is a lot of demand. On the ad, I put a sentence at the bottom saying if you are interested in this property please email me back with a few sentences about yourself and what you do for a living.
When there are a lot of responses, I will respond only to those who have taken the time to read the whole ad and respond in the manner requested. Usually, if you are not willing to read the full ad, you are not a serious prospective tenant.
Secondly, I will respond and set up a call for the following day at a time that works for them. This is another small test, if they cannot keep their schedule straight for our call the next day, they probably are not serious or can't pay rent on time. On this call, I just ask a few basic questions and let them speak and listen for anything that sounds off.