In fact, the scenes in which good ol' Forrest finds himself haphazardly in the middle of some of history's most important moments are all incredibly entertaining. If you're interested in finding out how it was done, as well as learning how to do it in your own films, this simple tutorial breaks it down in just 8 steps:

The Special Effects Supervisor on Forrest Gump, Ken Ralston, goes into detail about how he and his team approached adding Tom Hanks into archival footage. Unfortunately the video can't be embedded, but you can watch it here. (The bit about the technique starts at about 6:30.)

Probably the most important thing about combining two different pieces of video, whether it's archival or otherwise, is matching the color, lighting, and grain to the original. So, make sure you take note of what your archival footage looks like and try to determine how it was lit, angles used, if it was handheld, and quality of the image. If the archival footage you're using is old and you're using a newer camera to shoot your portion, you're going to have to degrade your image in post quite a bit to sell the effect. (There are plenty of film grain plugins you can use to do this -- FilmConvert is a great one.)

Source: Steve Ramsden