Some fabrics pill or shed little flubbers all over themselves. Ofcourse you can use a sticky roller but they are not as good as the next thing:
Step 1: Use a (old) Razor
Using your old razor is a great way to save some money and actually do a better job then with a sticky roller.
slightly pull your rasor down when your other hand holds the fabric tight.
Step 2: But Be Careful!
Be careful around the buttons and stitching because you can easily cut the fabric. But if you will be careful then you will end up with a new coat (or other piece of clothing)
Your welcome :D