Sivir is good for two reasons: Pushing power and using her ult to steamroll. Pick her with a juggernaut like Garen or Nasus on your team (divers that depend on movespeed boosts like Udyr or Shyvana also work well but they don't auto-win in melee range like true juggernauts)
Use Q and W to push the enemy back to their tower, ult so Garen can start spinning on top of the enemy and forcing them to run back, and if the enemy has their position off you can start bouncing ricochets off of some dummy for huge AoE damage, if they maintain good position and disengage then your team can just take the tower.
During lane you need good map awareness and knowledge of the matchup to know when you want to push the wave and when you want to back off. Your Q can poke for good damage but costs a lot of mana (especially with only one ability point in it, the damage isn't really worth it at that point) and W off the wave can usually land on the enemy duo or force them to split up. Your E is huge for making you capable of doing anything in lane by soaking an important enemy cooldown and then pressure while their skill is down. I recommend playing some bot games where you pretty much only focus on baiting out abilities from the bots and timing your spell shield, and you'll still need practice against real people before you can reliably pull it off.
As a champion with a shorter-than-average auto range and no dashes, she can have a lot of trouble in lane against champions with exceptional auto range (Caitlyn, Ashe, Jinx) but Sivir isn't really focused on winning the lane. If the enemy leaves lane to try and roam, backs due to your poke, or your jungler pulls off a good gank, Sivir can push quickly and get in some tower damage, but she's still just waiting until your team groups up and she can push that R button so your whole team suddenly dodges every skill shot and can run to exactly where the enemy doesn't want them to be.