I would say it varies a lot, depending on the breed. Larger breed often have hip issues. Smaller dogs with shorter muzzle have breathing issues. dogs with floppy ears tend to have more ear infections and ear mites. Other dog breeds have a tendency to very sensitive skin, which usually is rather easy to notice - scratching biting, inflamed skin, loosing hair, bald spots etc. Eye problems like the cherry eye are very common among dogs with a short compressed face, but other breeds can get it as well. It usually does not cause so much trouble but can cause the glands not to work properly and the eye to get dry, but it also can become really bad and even on both eyes - surgery (which is not cheap!) is highly recommended, often successful, but can fail as well and the cherry eye returns.
Some dog breeds have been bred to heavily that they are prone to certain diseases. I know that for instance the Saint Bernard has a lot of health issues and the Cavalier King Charles as well - those are breeds I know I never would choose due to their health issues and high chance of having to deal with some of them.
Treatment of the disease depends on too many factors you cannot just list - if the dog suffers just from one problem or several and also the severity of the issue.
Hip problems usually show when the dog has difficulty or even pain when moving, heart problems can show in various ways like heavy breathing, heart beat or even fainting or vomiting.
Breeds that have not been "worked" on too heavily usually have less health issues and even better off are the famous mutts, usually healthier than pure breed dogs and I can certainly stand behind that. I also experienced much better personalities in mutts, but that does not mean that you can't have an excellent pure breed dog.