Give him his space. Guys want space after a breakup. They want to be free. They want to forget about all the problems they had in the relationship. Give the guy plenty of time to forget about the negative aspects of your relationship.
Run into the guy you want back accidentally one day when he least expects it. Do this only after giving him weeks or even months to get over your relationship. If you have waited long enough, he'll remember only the good times when he sees you.
Keep the first accidental meeting short. You want the guy to think that you aren't thinking about him. Make it appear that it does not matter to you that you just ran into him. Say one or two nice things and let him say something if he wants, then leave.
Make an effort to run into him a second time a week or two later. Do this only if he hasn't called you after the first time you saw him. This second time you run into the guy you want back, strike up a conversation. Keep things very positive and smile a lot.
Ask the guy to call you one day. If you put the ball in his court, he can show you that he wants you back.
Play hard to get and act disinterested in him if it appears that he's not falling for you again. Keep doing this until you get him to want you back.