What does a typical function prologue and epilogue look like in x86-64?

The prologue sets up the function's stack frame (save %rbp, point it at the frame, reserve locals); the epilogue tears it back down before ret.

Every non-trivial function brackets its body with this setup/teardown so that the stack is left exactly as it was found.

With a frame pointer:

func:
    push %rbp          # save caller's frame pointer
    mov  %rsp, %rbp    # establish this frame's base
    sub  $32, %rsp     # reserve space for locals
    ...                # function body
    leave              # == mov %rbp,%rsp ; pop %rbp
    ret

Without a frame pointer (optimized): the compiler often skips %rbp entirely and just adjusts %rsp:

func:
    sub $24, %rsp      # reserve locals
    ...
    add $24, %rsp      # release them
    ret

Alignment subtlety: %rsp must be 16-byte aligned before a call. Since call itself pushes an 8-byte return address, a function begins with %rsp at 8 mod 16 — which is why local-space allocations are sized to restore 16-byte alignment before the next call.

Go deeper:

• Call stack (Wikipedia) — stack frames, frame pointers, and the save/restore bracketing.