How do you know if he wants to marry me?

By Asking him, If he says "No" then you will know he does not want to marry you, just make sure he knows your being serious.

Its the most effective way, men dont respond well to hints or indirect stuff, we are Direct creatures we prefer people be direct and honest when dealing with us.

Make sure.. if you love him dont scare him! I agree ask direct but let him know how hard it is for you to wrap your head around the whole idea of being locked in a bond with one person for the rest of your life, and let him hear your feelings about the commitment you made and vowed to uphold through the best and worst. If he cant keep eye contact or reveal his true feelings than what are you going to share for eternity... get the idea? this is the start of your new life he's holding back on now!!

Another answer:

Always assume that the worst thing a guy says is true. If he says "I never want to get married," he doesn't. And no amount of plotting on your part will change that. He'll assume that if he says it, and you still stick around, then you're okay with it. Ditto with "I don't want kids," "I have a wife," "I'm really into porn," and "I could spend all week playing WofW." All true. Live with it, or walk away, because it's never going to change. You've been warned.