Firts of all, have any of you done successful approaches for example at a grocery store or similar situation. I have tried to smile at women in grocery stores or walking by in malls, but they seem to be keeping to themselves and nerver see me. Is it more effective to just start a conversation with them in these situations? Any examples that have worked?

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Dude, if you wanted to learn how to do a standing back flip , you'd go to a gymnastics coach and ask.
He'd say "Swing your upper body backwards and kick your legs over" (or whtaever the fcuk he'd say).

But you wouldn't be able to do a backflip from that.

Broadly ,
Even if you don't have eye contact , if the woman has noticed your presence you can , from that point on go up to where she's trying to choose between brands of liguine (or whatever) and say something hilarious (it's best if one of the brands of liguine is under a brand name that rhymes with a part of the female anatomy but otherwise you'll have to think of something fybnny to say yourself). From that point even if she likes you you'll have to carry the conversation for 2 or 3 minutes.

The best way to get good at this is practice.And it's scary.

Good hunting to you.

First of all, FORGET about trying to win a woman over by eye-contact alone. In the real world, women simply AREN'T going to walk by you and look you in the eye. You HAVE to "interrupt" them. Ask them if they go to school in the area, or if they work out. I'm by no means a master, but I've made some attempts. Here are some threads about my experiences:

http://www.sosuave.com/vBulletin/showthread.php?s=&threadid=26309

http://www.sosuave.com/vBulletin/showthread.php?s=&threadid=28369