Depends on the instruction cacheing on the chip. IIRC, CPUs like Z80 don't have an instruction cache and have to re-read every instruction from RAM every time. 68000 (or was it MIPS4000?) has a 4 instruction cache so if there's a tight loop it might not have to re-fetch anything. Newer Intel CPUs have 10s or 100s of instructions in local caches.
So the fetch decode execute cycle is about as simple as the CPU can be described, fetch the instruction, decode it (which might mean all sorts of things, like fetching data from RAM) and then execute the result (which might mean storing data back to RAM). In a modern Intel, there might be as many as a dozen instructions being executed at once, at various stages of completion (super pipelining).
Jim