Computers strictly speaking don't 'know' anything, they simply follow the rules we define in software to whatever their conclusion may be. Even something like ChatGPT which appears to 'know' how to speak English is really just an enormous pile of maths.

As for what's happening on a physical level, the rawest material of a computer is a transistor. In the context of computers you can think of a transistor as a switch, electricity flows through the transistor but this flow can be turned on or off with another electrical signal. This gives us two distinct states our 'switch' can be in, which we can represent mathematically as the digits 0 and 1.

We can choose to say 'when the voltage is more than x volts it's a 1, and when it's less than y volts it's a 0' but this is very much our choice, not the computer's. Our use of the number 10 as the base (ie where numbers 'slide over' to the next significant figure) is also an arbitrary choice based on the fact we have 10 fingers, with binary numbers we use 2 as the base rather than 10 as its more practical. However, whether we choose to represent the number twenty two in decimal as 20 + 2 = 22 or in binary as 10000 (16) + 100 (4) + 10 (2) = 10110 it's the same number.

Transistors that take these binary inputs and outputs can be arranged into logic gates, their job is to perform logical operations on these binary numbers. An example would be an AND gate, it has two inputs and one output. The output is 1 if the inputs are both 1, but otherwise it outputs 0. Using these logic gates we can do maths, certain arrangements of logic gates can do binary addition or subtraction for example.

A CPU contains many of these arrangements of logic gates, all with specific purposes. You have things like registers, cache, clocks and so on all which all play a role in handling the logical operations the processor can do - many of these rely on precise timing. These are defined in an 'instruction set' which is a description of all the things you can tell the CPU to do. This is 'low level', it speaks entirely in terms of what binary numbers you need to give to a specific processor to make it do a specific bit of maths.

When a programmer writes software, they describe the maths they want the computer to perform in a 'high level' language which means they don't care about the ins and outs of the specific instructions a processor needs, instead they write in a langauge easier for humans to understand. There's many different high level programming languages for different programming tasks, but they all have to be turned into a specific sequence of binary numbers the processor will blindly eat through - following the logic to its arbitrary conclusion.

When the programmer wants to run their high level code, they use compilers and assemblers which are programs designed to automatically translate their high level languages to the low level 'machine code' defined in the instruction set. This would be extremely tedious to do by hand, for the same reason you don't mow your lawn with a pair of nail scissors.

This is an extremely oversimplified version of what's going on (from a software guy rather than a hardware guy no less), but the machine doesn't 'know' anything other than the logic gates that were etched into it when it was made according to its instruction set. At the end of the day it's just electricity representing maths, with limitless time and space you could do anything a computer does with pen and paper!