Simply put, photography montage is the process of making a composite photo from several different photographs. The process has been in use since the mid eighteen hundreds and took place in the photographer's darkroom. These techniques were untried and new and no doubt took a great deal of patience, trial and error. The photographer's skill was paramount as he manipulated negatives of different subjects and printed them on to the same piece of photography paper. The end result was a picture of illusion where people and things printed on the photograph were not really there.
Although the darkroom is fast becoming a thing of the past with the digital age of photography, the techniques are still in use albeit in an altered state. Photos are 'stitched' together to produce a panoramic view of the subject (typically a landscape), people are added or erased from a picture and, as in the past, a number of pictures can be combined into a photograph montage before the printing stage.
The sort of effect that this type of editing produces has been popular for as long as photographs have been accessible to everyone and makers of photo frames have tried to pick-up on this by producing frames where multiple photographs can be displayed within the same frame. It works well for families where several children can be featured or where the age progression of just one child can be seen at a glance.
However, back to the digital age of photography and modern day techniques. Software such as Photoshop or The Gimp allow us to manipulate images, so with the right skills it becomes incredibly easy to produce a photography montage that is plausible and worthy of any collector of photographs. But then a paper photograph is just a paper photograph and unless it is put into a frame it is unlikely to ever be on display.
New techniques are being developed all the time where photos can be printed on media other than paper such as photos on mugs and plates, metal and canvas boards and more - the process is so dynamic and progressive. The printing process is what separates amateur from professional as specialised inks and commercial products are likely to be needed, and they are just not cost effective for occasional use. The comparison between what you may print on your standard inkjet printer and what the professional prints will therefore be vastly different and will potentially spoil your whole project.