How does the internet get from the landing point of a sub-ocean cable and to your home router, step by step?
You need to first understand what the internet is. The internet is not a resource or a specific place or entity. Rather, the internet is an international network of devices. Your phone, your cousin’s laptop and your neighbor’s internet-connected washing machine are all part of the internet, as are the servers they connect to, such as Reddit and Facebook and your local town’s website that hasn’t changed since the late 90s.
So, the more correct question is to ask how are all of these different things connected. They are mostly connected with wires (copper or fiber optic cable), and sometimes with radio waves (e.g 4G, Wifi, Bluetooth, satellite connections etc).
To massively simplify things: each device in the internet can send messages to each other, such as “give the front page of reddit.com” or “tell me the IP address of wikipedia.org”. Messages can be split into smaller messages, but eventually they are combined back to the original form by the receiver. Each message contains the address of the recipient just like a letter, except instead of a street address it identifies a certain computer in either a local network or the entire internet. These messages are just numbers, usually encoded as binary (a numbering system where instead of having digits 0-9 there is just 0 and 1). The messages are routed by a massive network of routers, switches, firewalls and other devices, which read the address of each message and route it towards the correct destination. Billions (if not trillions) of these messages travel around the internet each second.
The landing point of a sub-ocean cable is still (for all intents and purposes) a router. From there to your house it just goes through a series of smaller and smaller routers, the entire internet can be reduced to an interconnected… well… network of routers.
Think of it like going to the beach with your parents.
On the way home, you drive through a series of roads and highways, eqch one gradually getting a little smaller, until you turn into your driveway.
Except it’s an autonmous (self driving) car
And at each turn, a traffic director tells your car which street to be on.