One point to nitpick here - the '94 AWB only banned the specified things made *after* the effective date of the law. Everything already in circulation prior to the law was grandfathered in, meaning there was a fairly large supply of "pre-ban" items on the market that were perfectly legal.
Enforcement was reasonably straightforward - manufacturers were no longer allowed to produce the prohibited items, and importers weren't allowed to import said items. Because of the grandfathering, a large supply of items that would otherwise be banned remained in circulation (albeit at inflated prices), and, as has been the case since with many state-level restrictions, it was possible for individuals to occasionally sneak by with post-ban items by keeping a low profile and betting on the fact that the police aren't actively going around checking everyone's guns for legality. Instead, the target was the suppliers themselves, as many of the things that made a gun an "assault weapon" were largely aesthetic features that were non-trivial at the time for an individual to produce. Manufacturers and importers had a variety of regulations they had to adhere to even prior to the AWB, and the bureaucratic structure to vet and approve new firearms designs already existed by the time the AWB was passed.
While regulators were relatively successful at getting suppliers to adhere to the letter of the law, the spirit of the law was very much not followed by gun suppliers or the gun-owning community as a whole. Many gun suppliers impacted by the AWB made significant efforts to legally circumvent restrictions through minor redesigns of their guns. As the definition of an "Assault Weapon" under the new law was defined largely by aesthetic and ergonomic features rather than function, manufacturers often merely replaced or omitted a few non-critical features to make the gun legal. This included things like using a fixed instead of adjustable stock on an AR-15 and omitting the bayonet lug and muzzle device. More commonly, the law had specified pistol grips as a "bad" feature, but had omitted thumbhole stocks, so many manufacturers would replace the more traditional stocks and pistol grips of their designs with single-piece thumbhole stocks (see AWB-era MAK-90s).