Each opcode will consist of an instruction of N bytes, which then expects the subsequent M bytes to be data (memory pointers etc.). So the CPU uses each opcode to determine how manyof the following bytes are data.
Certainly for old processors (e.g. old 8-bit types such as 6502 and the like) there was no differentiation. You would normally point the program counter to the beginning of the program in memory and that would reference data from somewhere else in memory, but program/data were stored as simple 8-bit values. The processor itself couldn't differentiate between the two.
It was perfectly possible to point the program counter at what had deemed as data, and in fact I remember an old college tutorial where my professor did exactly that, and we had to point the mistake out to him. His response was "but that's data! It can't execute that! Can it?", at which point I populated our data with valid opcodes to prove that, indeed, it could.