You'll want to stitch them down with cotton thread that blends with the color of the linen.
I'm sure there are framers who have found a more efficient way to stitch textiles down than the way I do it. I find it useful to use a brad in a small power drill (actually a cordless screwdriver with a chuck) to pre-drill the holes in the suede.
I'll thread a manageable length of thread, push it up through a hole, loop it through the textile and then back through the same hole. When I run out of thread, I'll temporarily secure the loose ends on the back of the board with framer's tape.
When I've done enough stitches to secure the textile the way I want, I'll go around with PVA adhesive on a q-tip and put little dabs on the threads close to each hole (on the back of the board!) to secure it when the tape lets go. Then I'll back the whole thing with ArtCare foam or Coroplast.
Maybe I'll take a class in Atlanta and find out how many hours I've wasted in 26 years of doing it this way.