If you're curious about orbital space mechanics, try Kerbal Space Program. You'll get a much better idea how NASA puts things into orbit after you've done it a few times yourself.

Basically, the rocket doesn't just fire in a straight line away from the Earth all the way into orbit. It starts arcing very soon into the ascent, and the thrust is nearly parallel to the Earth's surface for much of the journey.

The same way that you can push a ball just to the top of a hill. Very carefully, because if you push it too hard it will roll down the other side.

Check out https://en.wikipedia.org/wiki/Newton%27s_cannonball and http://www.scilogs.eu/en/blog/go-for-launch/2009-05-28/how-t.... To fly to the L2 point, you have to get your rocket into (an elliptical) orbit around the Sun that intersects with the L2 point. Once you get to L2, you have to match its velocity, which you do by firing your engines to speed up (or slow down) such that your rocket and the L2 point have zero velocity relative to one another.

While Kerbal Space Program's physics simulation doesn't have Lagrange points, you can get a pretty good feel for how they work by performing any kind of in-orbit rendezvous.

Here's the main reasoning for placing it at L2: http://jwst.nasa.gov/orbit.html