How do you know when a photograph has been altered and to what degree from the original image?

Poorly done alterations can often be detected by enlarging areas of a digital photograph with image editing/viewing software and looking for tell-tale pixellation in suspected areas. Often, the pixels exhibit a noticeable transition in the range of the color palette in altered areas (the range of colors is markedly different).

Since you didn't specify digital or not: a printed image likely shows a delineation of some sort around anything that has been added before the altered image is reproduced. Altering could be interpreted to include where the resulting print was "burned in" or "dodged" during the printing exposure stage. This is pretty much undetectable unless over-done, and you probably were not asking about this anyway.

Aside from these visual clues, a trained eye can often detect inconsistencies in lighting, shadows or specular highlights. For example, shadows of objects may fall on their left, but one object casts no shadow or it is on the opposite side or it's angle is different. The same can be said for specular highlights such as reflected sunlight being or not being where it should.

Sometimes, the photograph is so well doctored that common sense or research is all that most of us can go by. For this, I'm reminded of the fantastic picture of a huge leaping shark that appeared to be ready to devour someone dangling on a rope ladder attached to a helicopter. Anything fantastic is suspect, in my opinion. While I could make a case for the fact that there are specular highlights on the helicopter (indicating the sun was behind the photographer and off to the left) yet there were none on the shark, Google is often the best tool to relegate such images to the hoax files.