It depends upon the CPU. For instance, the 8086 (on up) includes a bit in the condition code register to enable "single step mode" where it runs a single instr

It depends upon the CPU. For instance, the 8086 (on up) includes a bit in the condition code register to enable "single step mode" where it runs a single instruction then traps. It makes single stepping easy. Other CPUs don't have that. So on a 6502, to do single stepping, you write BRK (software interrupt) over the first byte of the next instruction. When handling the BRK, you write the original instruction back into memory, then insert BRK at the next instruction. The hard part in all this is finding the next instruction. Not only do you have to decode the instructions to find it, but you also have to handle conditional branches, which either involves figuring out which path with be taken and inserting the BRK in the appropriate location, or inserting the BRK into both paths (and having to restore both later). This also precludes single stepping through ROM.