About 4-6 layers of free hanging carpet remnants will stop field point arrows. Not so good at stopping broadheads though. Drive a couple of fence posts into the ground, however far apart you want your backstop to be wide, then tie a wire between them and hang the remnant over the wire. Put another one or two sets behind that one, leaving about a foot between them. If that doesn't stop your arrows, add another.
About the only thing that'll do good and last a long time with broadheads - and let you get your arrow back undamaged
- is either a pile of clean sand or a turf butt, and naturally they'll both work with field points too.