First, unless you are willing to do a lot of work and groundbreaking for others, it needs to already specifically be supported by a Linux distro.
Without this support, you're looking at installing a distro, or just Linux in general, without the help of that or any distro's installer. Your first problem that you need to solve is that you need some type of disk-like device to store files. What kind of storage is available in the camera? How can you format it to ext2 or similar so Linux can store its files on it, without bricking the device? These are only the beginning of the problems you'll need to solve if no one else has done it yet.
Many devices not intended to run Linux are "hacked" into doing so through one of the following methods:
Device accepts any code as a firmware update: a modified firmware is installed as an update which either contains a Linux kernel + supporting files or a bootloader allowing installation. Many devices with a web-accessible interface will allow you to update the firmware through that interface. Some devices can be put in a service, management, or "rescue" mode which allows the same. Note that some devices only accept signed updates which complicates or prevents such hacking.
An existing vulnerability in the device's software is taken advantage of somehow, which allows custom code to run which then installs Linux. The original XBox is a classic example where loading a modified savegame into the original version of Mech Assault was the gateway to "softmods", including Linux installation.
It's possible that the device won't run Linux. It may not have enough storage space for a kernel (generally at least 4MBytes of flash or similar is needed), not enough RAM to do anything useful, and/or the CPU may not be supported, or it may not have features required by Linux (such as an MMU).