You don't necessarily have to beat her in lane. If you can out shove her and roam, you don't even need to beat her in lane, you just out roam her and snowball your team.
Laning versus Orianna requires you to keep careful track of both her and her ball. Smart Orianna players will park the ball a bit outside of it's cast range on your side of the creep wave, and then wait for you to step up and try to cs (or trade with her). When you do, they will step up so that your destination is in their Q's cast range and then cast it and back away. If you try to run at her, the ball will hit you and she will likely add her W to the mix for more damage unless she is currently low on mana or otherwise feels inclined to not cast it. You can bait this out by feigning moving up early and then dodging her Q when she goes for the harass, it's cooldown and mana cost are both pretty low though, so your window to exploit the fact that she just moved the ball is short (6 to 3 seconds base, depending on her Q rank).
The thing to keep in mind when trying to avoid being hit by her ball is that, like any other projectile skill, it her Q, Command: Attack, has a travel speed, and hence the further the ball is from you, the longer it will take to reach you, giving you more time to react and move out of its path. You can exploit the usual 'ball-parking' strategy a bit by first approaching from one side of the lane to bait out her Q, then once baited, move to the far side of the lane, maximizing its travel time should she try to cast it on you again. Moreover, if/when she does, simply switch sides of the lane again.
The other thing to be keenly aware of is her passive. It makes trading basic attacks with her counterproductive for most AP mid laners as she will win basic attack trades against them handedly. For this reason, it is preferable to stick to short trades against Orianna (or all-ins if you have the burst/DPS).