Believe It or Not...
Your grip will impact quite a lot; range of motion, release point, accuracy, finesse, and power to name a few right off the cusp. I'm sure I'm missing something, but if it comes to me I'll be sure to let you know.
1. Location... Location... Location...
Use your elbow as a reference and place the butt end of the stick up against it, so your dominant hand is about a forearm's length up the stick. This will give a nice balance of power and control.
Generally speaking, the lower the top hand, the more leverage + power.
The higher the top hand, the more finesse + control.
When passing, your hand should slide up the shaft by about a fist's distance. When shooting; back down. Play around for a bit and then place some athletic tape around your two sweet

2. Ride the Line
While the stick is laying on the underside of your forearm, let it pass over the heel of your palm, and into the valley that naturally forms as your dominant hand begins to grasp the stick. If you do this correctly, you'll notice a few things occur:
a) Your pointer finger will take the shape of a "trigger finger" and raise up along the shaft.
b) There's (most likely) a line on your palm that the goes from the middle of the heel of your hand towards the bottom knuckle of your pointer finger- this is your lacrosse line (yes, you were born for lacrosse).

3. No Handshakes
With the shaft on your lacrosse line, you'll notice your wrist will stabilize into a motion of a top-down / forward-backward motion (depending on how you look at it). If you are familiar with basketball, it's similar to the directional wrist motion behind a jump shot.
More importantly, this grip reduces side to side motion in your wrist (as you would get from a handshake grip), and it keeps things snapping in the direction of your target.
Picture your hand snapping towards your target and the head of the stick will follow.

That's all for now.
If you found this useful, pass it along to a friend!
-PeoplesLacrosse.com