depends how you wish to go about it...
as has been noted you'll have to use some Video Composition Software,
alot of professionals use Shake by Apple, this is because Shake has the ability to interface directly into the software you use...
Max/Maya/XSI/Houdini/Mirai and render via a 3rd party suchas Renderman, Messiah:Render or Mental Ray
however this said the price is $4,999; even i have an older version cause it's just so damn expensive.
A cheaper one is Adobe Premier Pro as this'll edit video nicely, and is around $350 last time i checked.
But really for an amature production even that is a little much.
There is always doing it in Max itself, it won't have quite the same effects; but you can use the video ram layer to project the video as you're rendering your scene almost like a background really.
This all said, you really need to sync both realtime and cinematic video stream; similar lighting rigs, camera positions, etc... else you could find it looking really bad really quickly.
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