There are hanging strops and paddle strops (and others). For daily use, I would say most use a hanging strop. You do mount it to a hook of some kind (or doorknob, etc). The strop will bow a little, but you pull it somewhat tight to ensure you don't round the edge.

Generally, I would say most use the linen then leather. The value of the linen is debatable. Many don't use it at all.

For a new str8 shave, one of the best investments you can make is Lynn's DVD, The World of Straight Razors. Its over three hours of very useful information. It will answer many common questions and the visuals really help. Best of luck!

Jordan