If it is just a few small areas of stain (especially if coffee), I would try Grandma's Secret Spot Remover:
http://www.amazon.com/Grandmas-Secre...dp/B0021JD2S0/
You would want to rub this into the stain with your finger or a soft old toothbrush, let sit for recommended time (15-30 minutes, I think), then wash the quilt.
If you use the "search" engine here, you should find several previous threads on how to safely wash a quilt. My recommendation is to use a top-loading washing machine, fill with water and soap (Orvus is good), stop the machine, add the quilt, hand agitate by pushing down on the quilt, advance the machine to spin cycle, spin out the water, fill with rinse water, again stop the machine and hand agitate, advance to spin. The important thing about using a top-loader is, if it has a central agitator (most except for some new ones do), never let the machine agitate the quilt. Do it by hand.
To dry, you can use a large dryer at a laundromat or even a home dryer -- provided it is big enough to allow the quilt to fall back on itself when tumbling. (If the quilt is so tight in the dryer that it can't move, it can develop burn spots from the air openings in the drum.) Or, you can lay out a large flat sheet on a carpet or outdoors (in the shade only, to limit sun exposure which fades some fabrics very quickly) and spread the quilt out on that. If indoors, add a fan to speed drying and turn the quilt over once in awhile. If outdoors, be sure to cover with another flat sheet anchored at corners with rocks; this protects the quilt from errant bird droppings. The trick with drying is to either use a large dryer or lay the quilt out on a flat surface to dry. You do not want to hang the quilt from a clothesline; water adds a lot of weight to the quilt, and a hanging quilt puts enormous stress on the hand quilting stitches that are close to the clothesline. You do not want to stress the hand quilting stitches.