How does machine code communicate with processor?
That's called microcode. It's the code in the CPU that reads machine code instructions and translate that into low level data flow.
When the CPU for example encounters the add instruction, the microcode describes how it should get the two values, feed them to the ALU to do the calculation, and where to put the result.
Machine-code does not "communicate with the processor".
Rather, the processor "knows how to evaluate" machine-code. In the [widespread] Von Neumann architecture this machine-code (program) can be thought of as an index-able array of where each cell contains a machine-code instruction (or data, but let's ignore that for now).
The CPU "looks" at the current instruction (often identified by the PC or Program Counter) and decides what to do (this can either be done directly with transistors/"bare-metal", or it be translated to even lower-level code): this is known as the fetch-decode-execute cycle.
When the instructions are executed side-effects occur such as setting a control flag, putting a value in a register, or jumping to a different index (changing the PC) in the program, etc. See this simple overview of a CPU which covers the above a little bit better.
It is the evaluation of each instruction -- as it is encountered -- and the interaction of side-effects that results in the operation of a traditional processor.
(Of course, modern CPUs are very complex and do lots of neat tricky things!)
Electricity. Circuits, memory, and logic gates.
Also, I believe Python is usually interpreted, not compiled through C → assembly → machine code.
If I am not mistaken, when you program in it, the computer first "translates" the code to C.
No it doesn't. C is nothing special except that it's the most widespread programming language used for system programming.
The Python interpreter translates the Python code into so called P-Code that's executed by a virtual machine. This virtual machine is the actual interpreter which reads P-Code and every blip of P-Code makes the interpreter execute a predefined codepath. This is not very unlike how native binary machine code controls a CPU. A more modern approach is to translate the P-Code into native machine code.
The CPython interpreter itself is written in C and has been compiled into a native binary. Basically a native binary is just a long series of numbers (opcodes) where each number designates a certain operation. Some opcodes tell the machine that a defined count of numbers following it are not opcodes but parameters.
The CPU itself contains a so called instruction decoder, which reads the native binary number by number and for each opcode it reads it gives power to the circuit of the CPU that implement this particular opcode. there are opcodes, that address memory, opcodes that load data from memory into registers and so on.
how does the processor process its instructions, how does it "find out" what to do?
For every opcode, which is just a binary pattern, there is its own circuit on the CPU. If the pattern of the opcode matches the "switch" that enables this opcode, its circuit processes it.
Here's a WikiBook about it: http://en.wikibooks.org/wiki/Microprocessor_Design
A few years ago some guy built a whole, working computer from simple function logic and memory ICs, i.e. no microcontroller or similar involved. The whole project called "Big Mess o' Wires" was more or less a CPU built from scratch. The only thing nerdier would have been building that thing from single transistors (which actually wasn't that much more difficult). He also provides a simulator which allows you to see how the CPU works internally, decoding each instruction and executing it: Big Mess o' Wires Simulator
EDIT: Ever since I originally wrote that answer, building a fully fledged CPU from modern, discrete components has been done: For your considereation a MOS6502 (the CPU that powered the Apple II, Commodore C64, NES, BBC Micro and many more) built from discetes: https://monster6502.com/