I've found that men rarely pay any attention to my wedding ring. They assume if I'm flirting with them, I'm available. One guy, even after I Facebook friended him where my status clearly says "married," still assumed I was separated, as I was so obviously flirting with him.
I have learned to say as soon as I know I'm interested: "I'm married, but that doesn't mean I don't want to get to know you. My husband and I have an understanding."
I've had little trouble finding people (especially men) willing to have a sexual relationship with a married woman. Finding people willing to forge an emotional connection as well has been more difficult. If you have a polyamorous community where you live, you might have better luck finding people willing to form emotional as well as sexual connections.