I saw a really attractive girl at the mall yesterday.

Just wait out on the block until closing time...
Follow her home...
Stand on the hood of your car with a boombox and wake her up in the morning...you cant go wrong bro!
Ive seen it work before...

As someone who worked in customer service for years, the girl in the mall is almost obligated to be nice to strangers while working on the clock. This would be the perfect opportunity to strike up a conversation with someone you otherwise would not have a clear opportunity to chat with. As far as what to talk about, you can never go wrong asking for reccomendation on merchandize or in this case anime or video game recommendation. Just be natural and try not to be too creepy, and she will gladly acknowledge you.

Make plans to see a movie with a friend or relative at the nearest movie theater. Stop in a few days before. Then tell her that you're going to see a movie in a few days and try to get her opinion of the theater. This should lead to a conversation.

If she says, "I go there with my sweetums all the time," you get the picture (no pun intended).

If she says, "I haven't been to the movies in a long time," she may be hoping to be invited along.

If she says she's not into movies, switch to talking aboot books or music or food. If none of those work, stick to pokemons and hello kitty stuff.

If she does neither, just let the conversation happen. Pay attention to any likes or dislikes.

And for crying out loud, don't go in there like you're waiting for something to happen. Go in there like you have places to go, giving her the opportunity to be the one who talks to keep you there.

Tell her you're going to get a bite to eat. Then disappear. Then come back another time. Again, tell her you're going to go get a bite to eat, but this time aks if she's hungry.

And if you're going to compliment her on something, compliment her on her shoes. And hold your farts in during the early stages.