Cleaning a vintage quilt takes time and patience, but it can be done. Just be aware that not all the stains will come out, and whatever you do, do not use bleach or scrub it in any way!
1. If it has mold/mildew on it, you'll first need to use Biz. Fill a bathtub with cold water, and dump about 5 scoops of Biz into the bath; mix to dissolve. Gently place the quilt in the bath enough to let it get wet. For best results, soak it 3+ days, slightly agitating the water twice a day. Do this by just moving the water around a bit with your hands. This will allow the Biz to not sink to the bottom. After the alotted time, drain; fill tub again with cold water and gently agitate the quilt. Drain & repeat about 3 times to insure all the Biz is out.
2. If it is just dirty, again fill a bathtub with cold water. I then place one scoop of Ivory Snow flakes in the water and agitate to dissolve. Place the quilt in the bath and get wet. Soak for about 1 - 2 days, agitating water twice a day. Rinse as described above.
(Quilt shops do sell a special quilt wash, but I have always had good results with the Ivory Snow. It's extremely gentle and a whole lot cheaper than the quilt wash.)
3. Let the quilt sit in the bath about 1/2 hour or so to let as much of the excess water drain out. Do not squeeze or wring the quilt, for if the fabric is fragile it will rip.
4. Let your quilt air dry. Place clean sheets on the grass in the shade, if possible, and lay the quilt onto the sheets. Cover with extra sheets if it is in full sun. This is to keep the fabric from fading. Turn after a couple of hours. If you don't have an outside yard, you can gently hang it from your shower curtain rod -- just make sure you have towels or buckets underneath to catch the water.
I hope this helps! If you don't want to try this yourself, you could always contact a local quilt shop to see if they know of anyone who will. It's worth a try.