I personally have a passion for antique table linen and usually can find great pieces in less august settings. Therefore, these pieces are sometimes in less than perfect condition. Double, triple and quadruple damask (categories which denote successive levels of thread quantity, the higher the better) in less than perfect condition are usually redeemable.
Most old linen is yellowed due to oxidation, and sometimes spotted due to improper or ineffective prior cleaning and storage. The cleaning process like the aging process will not achieve perfection over night, but never fear; with patience you will see results.
Step One: Never, and that would be never, put your antique table linens in the washing machine. The fabric, in some cases, is much too fragile to withstand the ringer/spin action. Antique table linens must be done by hand.
Step Two: Use oxygen bleach like Oxiclean or Tide. Never use liquid bleach even if heavily diluted, as prolonged exposure to liquid bleach will literally eat the fabric. I personally get great results with Tide (and no, I am not getting a kickback for the recommendation). Always use powder, never liquid. Presoak the linens in lukewarm water prior to adding them to a detergent solution. This will loosen the fabric and actually get some superficial residual dirt out of the fabric.
Step Three: Add three cups detergent to one gallon of water. The water must be very hot to activate the detergent. Add one gallon of warm water to solution. Drop each item, one at a time, into the soapy water and stir as each item is added. Allow mildly soiled items to soak for two days, stirring occasionally, and heavily soiled or discolored upwards to a week. (If soaking for a week rinse out the linens by hand in warm water and repeat the process)
Step Four: If you are eco-friendly, you may consider 2 cups white vinegar plus one-quarter cup salt, plus one cup lemon juice to one gallon of cool water. Pre-wash spots with lemon juice and salt prior to soaking. Soak upwards to two days. Repeat, if necessary.
Step Five: After desired whitening is accomplished rinse the linens twice in clear warm water. Never wring out the fabric but instead squeeze out the water then place it in a towel, wrap the towel around the items and press gently. The towel will absorb more of the water.
Step Six: Drying. Line drying in full sun is the best way to dry the linens, or lay small items out on wadded towels. Make sure the damp linen does not come in contact with metal, either in the wash line of by using a hanger; the metal may discolor the linen. In some parts of the world placing the linen flat on the grass aides in the whitening process, as the combination of chlorophyll and sunlight is a natural whitener. If drying outside is not possible use a laundry rack, preferably one that is plastic or vinyl covered wood, as untreated wood may leave a mark. Never dry linens in the dryer, as it will break down the fibers, but if you must set the heat gauge to delicate and remove the linens while still damp to iron them.
Step Seven: Ironing and storage. If linens have been washed and are to be stored indefinitely do not use starch when ironing — this will potentially yellow the linen and defeat all your hard work. Instead using an iron with a linen setting (usually the hottest) mist your linens with water and iron dry. You can use some of the commercially-scented products to moisten the linen such as rosewater or verbena. Make sure the scented product is an essence not an old based extract.
Ironing in creases, especially in napkins and table clothes will, over time, break down the fibers. If the linen is monogrammed with a raised design or all over embroidered, turn the fabric over onto a folded towel or completely cover your ironing surface with a towel or double folded white bed sheet before ironing. This will keep the monogram or embroidery raised and not flatten it. It will also prevent the tip of the iron from possibly ripping the fabric around the monogram.
Before storing make sure the linens are completely dry. If stored damp the linen may mildew, and that is virtually impossible to remove. If possible napkins, placemats and table clothes should be rolled over a tube.
For long time storage small items can be wrapped in acid free paper sleeves, or sheets of acid free paper can be used for larger items. For short time storage, place in a drawer or closet in a climate controlled environment.
Note: I love old wives tales about cleaning. If you have a great hint, I invite you to write in.