You beat LeBlanc through macro play, not micro play. Your job is to survive and not feed her gold while denying her minion gold so when the late-game rolls around, she can't get anything done.
Before the game starts, take an adaptive damage rune, an MR rune, and a health rune. The extra tankiness will help you survive her combo and keep you in the game. Consider runes like Nullifying Orb or Bone Plating to give you an even better defensive edge.
Shove the wave. LeBlanc's only waveclear is her W, which also happens to be her engage, disengage, and damage tool. In order to match your clear, she needs to W the minion wave (i.e., not you) in order to keep the wave from crashing into her tower. Once she uses it, you can start harassing her with autos and spells to get her health too low to commit. If you think she's going to kill a minion for CS, make sure she has to pay health or mana to get it, especially cannons. When your wave has more minions than hers, you are free to start attacking her instead of the wave.
Don't be too aggressive. If you just mindlessly shove, she's gonna root you when her jungler comes for an easy gank. Push the wave into tower, then back up unless you are absolutely certain of the enemy jungler's location. Use that free time to place deep wards so you know when you have the opportunity to stay and harass her while she cleans up the wave, or go back and buy.
Itemize against her. Your best bet is probably going to be Mercury Treads for the magic resist and lowered root duration. Banshee's Veil is a great pick since it not only gives you magic resist, but also a spell shield to soak up a part of her combo. Once you've finished your core item (for most mages, it's a Lost Chapter upgrade or Rod of Ages), start building MR so you don't die in the midgame when she's at her strongest.