I never understood how we can launch something into an L2 orbit. Does the rocket just fly out there and stop? Just it get caught at that location?

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.

That’s all well and good for most of the stuff humans do in space (and it really, really helps to get a sort of general, very basic and intuitive understanding of orbital mechanics), but KSP does not do Lagrange points at all. You cannot use it to get a basic understanding of how those work with KSP.

That's why our correspondent needs to install the Principia mod!

http://forum.kerbalspaceprogram.com/threads/68502-WIP-Princi...

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

Right I understand the reason. But as my question says, I don't understand how a rocket inserts it into that orbit.

This video shows the steps that take it from a folded-up thing stuffed into a rocket to a deployed telescope at L2: https://www.youtube.com/watch?v=bTxLAGchWnA The rocket is out of the picture fairly early on in the timeline.

Whoa. A deployment sequence to put Curiosity's one to shame. Too many moving parts, over the course of a month. I hope all goes well.

It's easier to think of it not as "stopped", but in an orbit around the earth that takes exactly 1 year to complete. So it does have some tangential velocity.