League of Legends jerks violently - what to do?

I'm trying my hand at League of Legends right now and I really like the game, however I just got into my first real round and couldn't really fight as it stutters all the time.

And although I'm just arriving at the opponent, I want to attack, everything stands still, and suddenly it works again and I'm dead immediately. It's absolutely no fun like that.

What can I do against it? Is that a bad internet connection or is my laptop too bad for it?

Can I do something about it?

Go to the settings and turn the quality and the FPS down.

You can easily look it up at the top right of the screen. You will then be shown FPS + Ping, with ctrl d or f