There are several ways to [attempt to] determine the veracity of an image, with respect to whether it represents a unique capture of a single scene:
Image data level inconsistencies
Certain processing operations result in telltale "signatures" embedded in the data which are often invisible to the eye but may be identified by statistical analysis. The best example of this is lossy image compression, e.g. JPEG. JPEG works in the frequency domain, removing frequencies that are below a certain threshold, depending on the level of compression. So if an image contains distinct areas with different patterns of missing frequencies, then it is highly likely that it is composed of separate images that were previously saved at different compression levels. This technique wont work in the case of high quality source images, or when the composite is saved at a much higher level of compression.
Repeated image content
A common method of removing objects works by copying the surrounding areas to cover something up. By identifying areas of an image that are identical to other areas is a sure sign of tampering. Even if the scene contains genuine repeated details they will differ in appearance due to scale/perspective/lighting/noise. A good example of this is the Iranian missile launch image, in which missiles are cloned to appear more numerous:
Some images are impossible due to inconsistencies in the lighting direction, i.e. if the scene is clearly lit from the left and one object casts a shadow to the left (toward the lightsource) then it is likely the object has been added artificially. Likewise with perspective, if you can see the top of one object but not another they are either not parallel, or one has been comped in. This type of analysis can be complicated when there are many lightsources, or if other parts of the scene are deceptive (surfaces are assumed to be flat when they are not). The moon landing photos have been implicated for having shadows in different directions, however shadow directions can differ when close to a lightsource, or when the surfaces receiving shadows are not parallel (such as the bumpy lunar surface). Likewise perspective analysis can fail when certain assumptions (such as objects are equal size, walls are parrellel etc.) are incorrect. Here is a famous example, the following image is not doctored:
It just looks wrong
This is the most common and at times the least reliable method. The brain is used to seeing real* image information from the eyes. Something in the image doesn't look real, it has failed some internal pattern matching. It could be a subtle inconsistency of lighting, it could be an apparent outline or some highly unusual shading. The first reason this approach is unreliable is that cameras don't work in the same way as the eye. The second reason is that people are now used to the idea that images are commonly manipulated, and will often look for inconsistencies that aren't there, they will overanalyse and anything that looks "odd" will be taken as evidence for manipulation.
Psychology / common sense
Finally you have to ask yourself if any motive exists for manipulation. Does the potential perpetrator have anything to gain? Is it even plausible that the photo is not real? The moon landings are another example of this - is it plausible that the number of people who must have been involved were able to remain silent for so long?
None of these techniques (except perhaps perspective inconsistency) apply to real, undoctored photographs of scenes which are themselves fake, or photographed in a way to deceive the viewer. A good example of this are the famous Cottingley_Fairies images. In this case the photographs were genuine, but the fairies were made of card!