Grape juice, like red wine, has certain pigments in it that are very hard to lighten and remove. Way back when, all I knew to do was to dampen the item with water and dish soap, scrub it as well as possible (ever try to scrub a feather pillow?), rinse out the soap, and then let it dry in the sun. If I'd gotten to it in a timely manner, that might have worked. As it was, the soiled pillow was untouched until the next day.
If you can get to it quickly, don't allow grape juice to dry on the garment. Once the fibers are dyed with the juice, it's very difficult to remove the grape juice stain.
There are a number of good products on the market that are quite successful in removing grape juice and other fruit juice stains. Clean-n-Brite is a dry granular stain remover than you mix with water and apply to the stain. The manufacturer claims it's the best for fruit juice stain removers. We haven't tried it.
We have tried Zout and Spray & Wash and found them to be effective if you apply it to the stain ASAP, and then work in either by rubbing between your knuckles or by using short quick strokes with an old toothbrush or other soft bristled brush. Allow to sit while the washer fills and then wash the garment per manufacturer's directions. I always air dry treated stains either by hanging on a hanger in my laundry room or by hanging the garment outside in full sun.
These days, I'm also recommending a treatment with white toothpaste - the kind recommended for whitening and brightening teeth. Moisten the stain and then squeeze out about a half inch of toothpaste directly onto the fabric. Scrub between your fingers; let the treated material sit for a half hour or more, then toss the garment into the washer and let the washer do the rest of the work for you.
These tips will also work for cherry, blueberry, blackberry, strawberry, raspberry, other fruit juices, and red wine stains too.