I wash all my quilts after I finish them. If a quilt is not too large I wash it by hand.
After washing, all the quilts go in the washing machine for a short cycle of spinning.
After that, if the quilt is small I lay it to dry on a flat surface.
If the surface I have is too small for the quilt, I usually hang the quilt to dry on this cardboard tube ( used by the fabric manufacturers for rolling the fabrics on it). I protect the cardboard (and the quilt) with a piece of nylon.
For bed quilts I have even a longer tube ( I brought it home from a carpet store).
I use the same tube if I want to bring my quilts somewhere. Instead of folding, I prefer to roll them.