CFN (continuous filament nylon) carpets are made of one long strand of fiber and will have next to no shedding.
When you first have a new carpet installed, you may notice that a great deal of fiber is coming up off the carpet. The good news is that this is not unusual and manufacturers factor in this "shedding" when they design carpets. The bad news is that you are going to have some steady, serious cleaning on your hands in order to get it to stop. Fortunately, in most cases, all it takes to stop new carpet shedding is some dedicated vacuuming and a lot of patience.
Check your vacuum to be sure it can do the job. You need a vacuum with at least 80 cfm (cubic feet of air per minute) vacuum power. This will help you lift the loose fibers right out of the carpet.
Vacuum the entire room before you replace the furniture. Use slow, methodical movements and make sure that you cover the entire room. As you walk around the room vacuuming, you will notice that more fuzz is coming up off the carpet. Finish the room before going back for a second pass.
Empty the vacuum bag and filter even if they are not clogged or filled. This will help your vacuum maintain steady suction.
Replace the furniture. Position it in such a way that you will be able to vacuum around furniture items like coffee tables.
Vacuum the room once a day. As people use the room, the carpet will continue to shed for several days to several weeks. Vacuuming each day will help minimize shedding until the process is complete.