Hand-wash the napkins in tepid water and mild soap designed for hand-laundering, for linens or for baby clothing. Rinse well and roll the items in a towel to remove excess water. Air dry them on a flat surface.
Soak the napkins in a water and mild soap mixture if a brief hand-washing isn't sufficient. Soak overnight or up to two to three days. Rinse them well, roll in a towel and air dry flat.
Hang the napkins in the sun if soaking doesn't do the trick. Set delicate fabrics in the shade or for brief periods.
Soak the napkins in water and an enzyme-based laundry booster or stain treatment if mild soap is ineffective. Follow the package instructions, rinse well and air dry flat. If an enzyme-based product doesn't work, try to soak the napkins in an oxygen-bleach solution.
Use chlorine bleach only as a last resort. It is effective but harsh and it may weaken fabrics or cause holes. It's worth a try on napkins that are useless if they can't be whitened. Use a tiny amount of bleach and a short soak time to minimize damage.