At least I started by playing around with microcontrollers (the ESP8266). From there you will get an understanding of how they work etc. Most of the time there’s an imprint of the chip type, so figuring out the type isn’t hard.

Dumping the firmware depends on the chip. While playing around with these chips you will also get to know the tools. In this case „esptool“.

For me, most of it is learning by doing and being curious how these systems work. At the start you may do wrong assumptions about the system. But the more you research the clearer it gets.

Generally there are established communication protocols, and developer debug hook points.

JTAG, UART as common interfaces.

I2C, CAN bus as protocols you're commonly going to find.

Stuff like Arduino, Raspberry PI are generally good introductions to embedded ptogramming and debugging.

Nothing beats having access to a hacker space where someone can mentor you during learning.

You can buy test/development kits for cheap (depending where you are in the world) that allow you to mess around and play with this kind of stuff.