Ben Eater on youtube has a great series
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This is not straight forward if you don't have the background. For starters, I wouldn't think about it in terms of logic gates. You wanna just think about it in terms of logic. Usually hardware is designed using verilog or vhdl which is converted into logic gates by software.
The general idea is you have a set of instructions that the CPU can understand. Each instruction would have a unique code. The CPU reads one operation at a time from memory, and each operation will be one of those supported commands. The CPU will figure out the operation and operands, and then start the processing. Different operations can take a different number of cycles. A simple CPU might wait for each operation to finish before proceeding. A good cpu will perform many operations in parallel and pipeline the results.
That's the gist of it.