My advertising vehicles are Craigslist, Trulia, Postlets, Zillow, Social Serve, Social media sites, a sign in the yard flyers e-mailed to contacts as wall as businesses and gencies in the area. The vehicle all depends on the type of house and neighborhood.
Before you even begin to talk to prospective tenants 1) understand your state laws as mentioned but 2) develop a selection criteria that you will follow for EACH prospective tenant. You must be consistent to avoid any thoughts of discrimination by applicants.
I have a scoring sheet that I follow and give points to each person based on income, years at job, credit history, years at previous residence, on time for showing, if application is complete filled in etc. You'll have to develop what works for you.
Do a pre-screen over the phone to minimize waisting your time on a showing. Ask questions like:
1. What are they looking for in house to make sure your place is a fit for them. Even if you have everything spelled out in your rental listing people still don't read.
2. Ask whats their income. Make sure at a minimum they qualify based on income.
3. Ask if they have pets b/c if you don't allow pets no point in waisting time.
4. Make sure they have a landlord reference you can call.
5. Ask if they have ever been evicted before.
6. Ask how many people would be moving in the rental.
7. Ask if they smoke
Next, after you prescreen and determine a person sounds like a good fit based on the above, schedule an appointment to show the rental. Require all potential applicants to call or text you one hour before the appointment. This will ensure they will show up. In the past I use to make appointments with people and they wouldn't show. Now I require they call me a hour ahead. If they do, I know they are serious. Believe me people will waist your time.
Lastly, always verify income, speak with their previous landlord, run a credit and eviction check, background check and at a minimum drive by their existing house if feasible. I've even done a personal house visit for some. I use a tenant screening from mr.landlord.com.
There are lots of professional tenants out there looking to get over so have your policies and procedures and stick to them.
Good luck!