I'd like to have a system in place which automatically imports financial stock values from an external source to my own site, after which I can make an alghoritm with javascript which makes calculations. But I don't know how I can import data from other websites to my own. Can anyone explain me how that works?
As I said in a comment you have to use their API. There are a lot of sites which show their API publicly e.g Twitter.
Simply put send a request to specific url and their servers will respond with the data which you can then process how you want it.