I have rental property as well as being an agent. I find tenants through http://www.craigslist.com.
Originally I used the local newspaper but I've found the craigslist works better. However, those were for properties in Atlanta, GA a big market. You can also put up signs in the local grocery store bulletin board.
The key word you use is "good" tenant. I always interview by phone. And if you really want to find out about a person just get them talking about themselves, what they are looking for, why they left where they were living. I never take a tenant who complains about the way the former place was managed, kept up because those folks will end up not liking your place any better, it seems.
Depending on the rent, I check out the credit history, criminal history of the person through a company that will do so for just $25. Contact me and I'll get you that email, name. It takes no time at all and will at least let you know if the person jumped ship on a former landlord.
Lastly, if it is someone who lives locally, I go and visit them at their current residency. In that way, I do a sniff test. Is the place kept clean, are there messes in their place that I wouldn't want in mine, is the garden kept up, dirty walls, pets I didnt know about. And then, too, after renting to folks for 30 years I go by my intuition. If I don't get a good feeling from them, I don't rent to them. After all, you are going to have to deal with these folks every month if for nothing else than to collect your rent and it can eat away at you if that becomes a hassle.