I used an improvised "Squeegee",....a 5" block of 1 x 1" hardwood, to iron the felt down, and stretch it.
One thing you DON'T want to do is start working that felt with rubber cement on your fingers.
.....sure nice to hit some common ground here,...based on a reverence for tools.
While I can't say I always hit the mark, I think that clean, sharp, and readily ACCESSIBLE tools make for better quality work, and finished projects.
GTC