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?
Cryptocurrency exchanges are generally taking custody of your funds while you are using their service. You send a deposit of fiat to their bank account or cryptocurrency to an address under their control and after this payment has been confirmed, they credit you a balance on their platform. When you trade one currency for another, they only update their liabilities to you in their database. Only when you withdraw, they send you the corresponding cryptocurrency to your address or wire you fiat.
As you see, the exchanges simply accounts for what they owe you and there is no need for various blockchains to communicate beyond the exchange sending and receiving payments in various currencies.
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.