Generally you would be talking about software installed to onboard flash, either Compact Flash through an IDE-adapter (in the case of using standard X86 hardware) or some onboard flash. You could use PXE, but that severely limits your flexibility and mobility, as you are then rather literally tethered to a master server of some type.
As for getting Linux ready for booting from flash/PXE/whatever, there is nothing you really need to do beyond slimming the installation down. By virtue of the way the Linux kernel works, there is no functional difference between installing it to a HDD or a Compact Flash card.
Though you will probably want to compress your filesystem, and run it from RAM, rather than running it directly from flash. This prevents excessive read/write from the media, and speeds things up considerably. It does mean you will need to have a decent amount of RAM in the device as well.
You might want to read
something like this to get an idea of how you can get started with a simple installation.
