I've learned that the different cryptocurrencies have their own P2P blockchain networks.
How do exchanges convert coins from one network into a coin on another network?
You cannot just exchange two cryptocurrencies with one another that easy.
You will need a middleman like an exchange to do this.
An alternative is Atomic swaps. But it's still more experimental.
You can learn more at it here:
Atomic Swaps have been implemented in the lightning Network(Just as proof of concept!!)
Nevertheless, it's just a proof of concept and experimental. Exchanging one coin for another is done either by exchange or by communicating on the real world.
The exchanges do not turn a cryptocurrency into another, they just buy and sell them for you to somebody else within the exchange. For swapping the coins there is the already mentioned experimental atomic swap technology which could be revolutionary and potentially disruptive for traditional exchanges.