We wash our own muslin the same way we tell customers to: cold water, gentle cycle, nothing fancy. The open weave in muslin cotton is what makes it breathable and quick drying, and that same loose weave is why it keeps getting softer the more you wash it. If the clothes are new, washing them before the first wear helps settle the fibers, though ours arrive pre-washed so they're already soft out of the bag.
Skip the fabric softener. It coats the fibers and works against the natural softening the weave already does on its own. For drying, tumble drying muslin on low heat is fine, or hang it to dry if you'd rather avoid the dryer altogether. High heat is the one thing to avoid, since it's harder on the fibers than the wash itself.
Expect some creasing, that's just how a loose, breathable weave behaves and it's not a sign anything's wrong. Our muslin is double layer, sewn with flat seams and finished with child safe dyes, with no harsh finishes to wash out before it feels right against skin. If you're weighing muslin against another fabric, how linen compares for washing and care is worth a look, since the two need slightly different handling.