I have the 4-C OXO Good Grips fat separator as well. While I prefer the glass units (for ease of cleaning), I've got by fine with this unit.
First step is to throw away the gray insert plastic "strainer". Thats right, brand new out of the package and into the trash...
While you're at it, you might consider ditching the almost equally useless stopper for the spout.
Before use, utilize a fine-mesh strainer to filter whatever fluids you're separating. Then use as directed above - waiting a minute or so before pouring off the juices. Pour slowly (and don't pour, then level off to check your progress, keep pouring as described below) and watch what is traveling out of the spout through the side of the spout. When you see some cloudy turbulence, right the separator to keep the fats from flowing out.
If you want you can practice by pouring in some water and vegetable oil. and pouring it off.
Make sure you have a $1 bottle brush to clean the interior of the spout lest you poison the family on meal two!