Look up the concept of a "Central Limit Order Book" (CLOB) -- this is the fundamental data structure that allows the matching and of buy- and sell-orders on a typical exchange "matching engine". It matches these orders in "price-time" priority.

Once you understand this, everything else, at least at a technical level, more or less falls into place, but you will need to learn a bit about the various order types (market, limit, etc), and the concept of "liquidity provision"

On top of that you can look at concepts like "Exchange Connectivity", "Market Data" Feeds, "Clearing" and "Central Counterparties", and, of course "FIX".

It will take time, but it'll all fit together in the end and you'll end up with a reference architecture for a prototypical exchange business reasonably easily after that.

Source: I worked in wholesale finance IT for over 2 decades, a good chunk of those in exchange / exchange-like businesses.