How does a multi-pump pneumatic work?

You operate a forearm-mounted lever (or a butt-mounted pump arm on some designs) several times to compress air into a small onboard reservoir.

Each pump adds a controlled amount of air. When you fire, all that stored air is released in a single shot, then the reservoir is empty until you pump again. The gun has no spring slamming forward and no cartridge to buy, which is why multi-pumps like the Benjamin 392/397 and Sheridan Blue Streak have stayed popular for over half a century.