Elise can be pretty dominant pretty early. Her Q provides some great harassment, and a great nuke in spider form, and her W makes her near impossible to fight with. Her stun is fairly long range, and you should always lead with it if possible. Focus on farming, and the occasional auto attack or Q harass, and then when you have an opening, stun them and go in for the kill. Your typical combo is (Human form) E,W,Q then R for spider form and Q,W and attack them to death, save rapel for if they flash or if you need a reprave from minion agro or whatever the case may be.

This is where Elise shines the most. She's almost impossible to 1v1 with her sustain and Nukes from her Q. USE THIS TO YOUR ADVANTAGE. You don't even have to fight them, just the threat that at any moment you can strike, should keep them on edge and afraid to CS. Something I can't stress enough is not shoving your lane. Simply put, if your lane is pushed, you can't get kills, or deny CS, in other words, you can't be effective. The only situation where you should push, is if you are losing, quickly clear the wave, then roam to other lanes.

Jump on the adc, burst them down, then try to take as many people down with you as you can. On a side note, you can solo baron once you have 4 or so of the core items.