You get a standard CO2 high pressure tank regulator (can buy online or wherever you buy the tank from)
You can run air tools no problem, as the flow rate on them is usually really high, as in your normal 12/24V compressor might be rated at 1-2 cubic feet per minute at 90psi for a decent compressor, these setups can do 40+ CFM at the same pressure.
the tank will be 700-900 PSI when full, so how high you inflate the tire to is entirely up to you, but easily more than enough to blow it up if you aren't careful.
One ten pound tank can fill a couple dozen decent sized tires before needing refilled.
Recently I saw a guy pull a scuba air tank out of his trunk, change the fitting on it, and use it to inflate his car. Exact same idea, just a different source of pressurized gas.
If you want to learn more, there are several commercial units out there you can take a look at. A little more expensive than assembling one yourself from individual pieces, but they will have everything you need and support to go with it.
Examples
(I'm not endorsing any of the below products, as I have a more than adequate air compressor setup)
(this link they have several charts showing about how many tires you can reinflate and what types of air tools and amount of use you can get out of different sized tanks)
Power Tank is the ultimate on-board and mobile air system for performance, versatility, and reliability and your source for all air related accessories.
powertank.com
CO2 tank tire inflations system and accessories. You can air up all 4 tires multiple times, run air tools, water pumps, etc. Giving you more self-sufficieny! Great for offroading
www.offroadairbuddy.com