There are several different ways that swimbladder disorders (SBD) can present, depending on the cause and severity.
The flippers: they just sort of tip or roll onto their backs. With some effort they can right themselves, but will flip again if they stop or slow down. They usually don't float at the surface. My personal experience with this type is that it's caused by a mild internal bacterial infection. You can treat it, temporarily, with antibacterial meds, but the best solution that I've found is a homemade gel food with part of an acidophilus tablet dissolved/mixed in (I feed my goldfish homemade gel food every morning, and it's done wonders for my flip-prone albino.)
The floaters: the fish float at the surface. Often this is a result of constipation, usually due to overfeeding. Some fasting and meals of deshelled peas are often enough to clear this up.
The flipped floaters: the fish float upside down at the surface. This can be a very severe situation. Again, constipation, internal bacterial infections, or a combonation could be the cause. Chances are there's more than just one bad thing going on. On the other hand, my blue/choco Moor recently had a bad habit of skimming the surface for leftovers (I only feed sinking foods, but some of the stuff had floaty crumbs), and was swallowing air to the point that she was floating upside down. This is why you should
never feed floating foods to compact-bodied breeds of goldfish. I figured out which foods were producing floaty crumbs and stopped feeding those.
The sinkers: the fish stay on the bottom. This usually follows a very severe round of flipped floating. At this point the swimbladder is most likely permanently damaged, and the fish's days are numbered. Some people have made buoyed slings for their unfortunate fish (you can find descriptions of and plans for those online), but there's not a whole lot that you can do.
The main things to do to prevent SBD are keep the water conditions as close to perfect as possible, and do NOT overfeed. Some fish will be more prone to it (like my albino with her bacterial infections, or Ryukins with their especially deep/compact bodies.)
There are other situations and causes, as well, so hopefully someone else will chime in and share their knowledge/experience.
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That's about the extent of mine off the top of my head.
Aside from SBD, goldfish can get just about any other common fish disease--finrot, ick, fungus, hole-in-the-head, parasites, dropsy, etc., etc., etc.