I find nearly all of mine on facebook buy/sell/trade pages.
Credit and background checks !
I've found that the first important step is setting a correct rent price. Renting your house/apartment at the low end of the market can invite trouble.
Once I feel I have an appropriate rent price, I require all of my prospective tenants to complete an application through an online credit check & tenant application website. I believe this costs them around $25. We also ask for proof of income in the way of pay stubs. The credit check site also runs background checks. Usually if a tenant is interested but has a troubled past (bad credit, evictions..), they won't even fill out the application - so usually once I receive a completed application it is a tenant with a good track record.
We have also asked for prior landlord phone numbers -- you would be surprised how much info some are willing to share. Learned our lesson one time not taking the advice from the previous landlord.
We make sure to be thorough and not skip any of these steps and it has worked out well for us.