Authorizing and getting access to a third party system

I need advice from the brightest minds here in this community. I am trying to build a web application which will go through a pre-existing commercial web application and fetch some data.

My idea is to ask for authorization for that system, the users will enter their username and password, and the system will automatically go to the user's account and get the required data.

My question is how to do this? Are there any pre-existing libraries that give similar functionality?