I got better at this by doing debate in high school. In most forms of debate, it's standard to take pieces of evidence and only read certain words to make it shorter and more concise.

The way I did it was this. I started with highlighting any sentences that provided information I considered essential to the article as a whole. Then I'd slowly just start bolding the stuff that was important from that. Then highlight everything from the bold that isn't redundant or bad writing. It was an endless loop for a while, but eventually I got to the point where I could just highlight with zero iteration because I got used to finding what is and isn't important.