I've been a big fan of sweaters for only a few years, and I'm sadly just learning about proper techniques for keeping them in shape. The first is one that I had to learn quickly, because the sweater I wore to see The Nutcracker was covered in fuzzy little pills, and I needed that to not be a thing, as you can imagine. Shaving a sweater seemed a bit ridiculous to me, but I feel like I've discovered something great (that most people probably already know, but I digress).
All you need is a regular razor (like one you'd use for shaving) and a flat surface. Make sure your sweater is laying completely flat, and shave downwards in short, quick strokes. It's still possible to rip the sweater, so do this carefully.
As you do this, you'll notice the fuzzy pills gathering. Just pull the loose chunks off and continue.
Not Shaved // Shaved
It's as simple as that, really.
I know another tip to keep sweaters nice is to go as long as you can between washes. Hand washing is probably best, but if you're like me and it isn't a practical option, wash your sweaters (in a machine) inside out with cold water, and lay them out flat to dry. I've also heard that keeping sweaters, like jeans, in a freezer between wears is helpful. I honestly haven't tested that one myself, but it's worth a shot.
I hope this was helpful!