It's safest to play just by last hitting until level two, however to ensure that you level before your opponents, I like to throw in a Boomerang Blade or two. Successfully hitting the enemy ADC with your Q forces them to play back a bit and zone themselves from experience and lose a few creep kills as well. As an AD Carry most of your gold comes from last hitting creep. I've seen enemy after enemy that I've forced to kill creep from behind their tower underestimate the range of Sivir's Q and get killed thinking they're safe. Take advantage of their over confidence in the early game.
With that early game strategy I very frequently take bottom tower before any other tower is taken on the map. This allows me to roam to objectives like Dragon and helping to pressure other lanes. When your lanes are pushed, your best move is to farm your jungle, the camps come up frequently enough that you won't be hurting your Jungler by taking a camp in between waves of creep and pressuring your teammates lanes. It may be a little too early to try to take a second tower in your own lane, but taking jungle creep allows you to continually gain experience and gold. You never want to be wandering around doing nothing, that other than feeding your opponents kills, is the quickest way to get behind in the game.
When you've got a few items built, and since you always have a ward on hand with your trinket, you can safely split push, keeping your creep score up and helping your team gain advantages by pressuring and taking objectives (towers) by now you can also solo dragon, so if you don't feel safe taking the deeper towers, when dragon is up go kill it while your enemy has other things to pay attention to.
As with any AD Carry, your positioning is key, you need to be in the back as you have the longest range and need to be protected by your allies. Like I mentioned before your ultimate is very useful in teamfights, it can secure kills by allowing you to catch up to enemies foolish enough to think they can flee, or if things get a little messy, it can be used to get your team to safety. When the enemy is grouped use Boomerang Blade and Ricochet to hit the most targets at once and inflict the most damage as fast as possible.