Question
Thanks so much!  One last thing.  I noticed when I added the salt (which I will now dilute until I get the right stuff)that possibly small red thready things came loose in a few places on his sides. It's possible that it's just sediment from the water (it's well water), but I was wondering what size parasites I should be looking for.  That spot (it's black, BYW, not red) is about the size of one scale, but the thready things are just a wisp, and could just be sediment coagulating because of the salt. Thanks so much for helping me, I feel so helpless when I see a fish on it's side like that!
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No, the scales are not sticking out, so I don't think it's dropsy.  I did try to feed him again, and he ate a few flakes quite voraciously, but he's still laying mostly on his side, curled in fish fetal position I guess.  I don't see any obvious injuries, though one scale mid-abdomen seems dark red (abnormally).  I put in aspirin out of desperation late last night (just a half, crushed) because it seems to be a cure-all for everything else.  I used pickling salt, rather than processed salt, I heard that was better.  I'll try adding more salt to the tub he's in, and leave it, see if that works.  Going to the store later, anything I can get that might help?

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After returning from a trip recently, I found my largest pond goldfish (about 7 inches) laying on his side several inches under the surface looking very bloated.  I put him in a separate container, and have given him one diluted saltwater treatment (about a teaspoon in 3-4 gallons) for 15 minutes this morning, then changed the water.  I put half an aspirin in the water last night, as well as gave him some food, though I'm not sure if he ate.  Today he seems even more bloated.  How often should I give him a saltwater treatment, if at all?  I read on another forum that feeding him baby peas (blanched and skinned) is like a laxative, and I should try that.  Any other suggestions or clarifications?
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Are the scales of the fish sticking out?  If so, then it's dropsy.  Dropsy is very hard to treat.  You can try aquarium salt and antibiotics but really only injected antibiotics will give the fish much hope.  The salt amount you can use is a tablespoon per 2 to 5 gallons, much more than you used in the treatment.  The fish can be left in that much salt in the water.  For salt water dips, the amount of salt would be a few tablespoons per gallon and only for 20 minutes or so.  I suggest doing about 1 tablespoon per 3 gallons long term instead of using salt dips which are better suited for things like making large external parasites let go of the fish.  Some people suggest using Epsom salts (magnesium sulfate) instead of regular salt (sodium chloride).  Why did you add aspirin?  It could do more harm than good.  

Feeding peas is to help with mild intestinal bloating, gas, and swim bladder disorder.  Not having seem a photo of your fish, I can't say if it's just truly bloated, has dropsy, has another internal bacterial infection, or has a kidney malfunction (see http://www.fishpondinfo.com/health5.htm ).  Peas should be cooked and peeled.  I hope your goldfish beats the odds and gets better!

Robyn
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Pickling salt is normally just more coarse sodium chloride.  Regular table salt is sodium chloride.  I buy cheap aquarium and pond salt, all just other forms of sodium chloride although some may contain dried down salt water which has other salts and things as well.  Aside from the salt, you might buy some antibiotics; I use Maracyn I by Mardel mostly which is erythromycin.  Some antibiotics like penicillin kill good bacteria but erythromycin does not.  You probably don't have an active biological filter in the quarantine anyway.  For that reason, keep an eye on the ammonia and nitrite levels and change a little bit of water every few days.  If you don't have test kits, get those at the store too.  Good luck!

Answer
Hopefully the red threads are just something that's not part of (or attached to) the fish.  I would check out photos of anchor worm to verify that you did not see anchor worms on the goldfish.  The larger parasites include water lice which look like dark or clear spots about the size of a scale (check out photos of those to rule that out too for that spot you saw), the anchor worm, and water leeches.  Most other parasites are too small to see with the naked eye.  A few, like ick, when in groups, appear as small spots.  If you send me photos of the spot and whispy things, I might be able to tell you more.