Some materials are bought new and slowly ruined. Others are bought new and slowly earned. Linen and waxed canvas are firmly in the second camp, and caring for them is mostly a matter of doing less.
Linen
Wash warm or cool, tumble dry low, and skip the fabric softener — it coats the fibers and dulls both the hand and the absorbency. Linen wants to soften on its own, and it will, a little more with every wash. Iron it warm if you like it crisp, or fold it straight from the dryer and let it relax.
Waxed canvas
Wipe it down with a damp cloth; never machine wash or dry-clean it, which strips the wax. Creases and a darkening patina are the point — they are the record of use. When the cloth eventually looks thirsty, a fresh coat of wax worked in with a hair dryer's warmth brings it right back.
The goal is not to keep these things looking new. It is to keep them working, and to let them look like yours.