So you got dumped. You still love her. You need her back. It's a nasty situation, and while I can't promise you your phone will start ringing the moment you read the last word of this 'tutorial' of sorts, I can at least give you five essential tips to improving your chances of getting her back.
Do NOT be all over her. In other words, don't bombard her with phone calls, texts, flowers, angel dust or whatever. You need to keep cool. If she notices that you're actually being cool about it, it will bother her. No girl likes dumping a guy and having them just get over it straight away. Girls want to be wanted, but keep it smooth.
If you feel up to it, date other girls. Don't get serious with them, but just go to the movies or to a mediocre, run of the mill restaurant, and make sure the girl you want back knows about it. Don't go and tell her straight out as if you're boasting, but maybe in an online chat conversation for example, just sort of push the conversation in that direction, like, "what are you doing tonight?" Then when she says, "oh, nothing really, you?" take your chance and say "oh just going to the movies with a new friend", or something along those lines. Lots of subtle hints is the way forward.
Remind her of what she's missing! Don't make it seem like you're being a total actor, but just be really cool and nice around her, treat her nicely, talk to her in a sweet way, etc. You have to remind her about the amazing side of you, because presumably she dumped you because you also have a side she really didn't like.
Go to places which are hotspots for meeting girls. I'm talking bars and clubs sort of thing, and again, make sure she knows about it. She may have dumped you, but as long as you don't do this step too late, she isn't gonna like the thought of another, possibly sexier girl having her hands all over you. But again, don't go overboard and make it look like you're purposely making her jealous.
It works the other way around too. Your girl that you just lost could be doing these things to you, but it's all about staying one step ahead. If she tells you she's going on a date with some guy, be cool and say, "nice, have a good time". Inside, you could be wanting to go kill whatever dude has got your girl, but as long as you seem genuinely cool about these things, she will not like it.
Lastly, just give it time. This won't... well, probably won't happen overnight. Stick at it, and don't blow it. It is very possible to get a girl back; and if you do, don't screw it up again. You might get lucky once, but it almost definately won't happen again, unless she is really dull, in which case I advise ignoring these steps and finding a woman with at least half a brain cell.