While the demo content and example programs still in development, you can start learning to use this mod by examples.
... or join discord community on the page https://mods.factorio.com/mod/fcpu/discussion

Tutorial videos

• Very good tutorials was made by BLU12 Gaming, see his YouTube channel.
• DocJade programmed a single assembler with fCPU to beat Factorio.

Example 1

It simply enumerates signals from red input wire and copies them in availabler registers from reg1 to reg7.
fCPU code:

clr
:loop
mod reg8 cnr
mod reg8 7
inc reg8
mov reg@8 red@8
sst reg8 reg@8
mov out1 reg8
jmp :loop

Example 2 (complex system for train management by Cid0rz)

https://github.com/cid0rz/CTS-Cidorz-Train-System

Example 3 (recursion)

mov r1 5
call :fib
hlt
jmp 1

; r1 = fib(r1)
:fib
  ble r1 1 :fib_base

  push r1
    dec r1
    call :fib
    mov r2 r1 ; r2 = fib(n-1)
  pop r1

  push r2
    sub r1 2
    call :fib ; r1 = fib(n-2)
  pop r2

  ; fib(n) = fib(n-1) + fib(n-2)
  add r1 r2
:fib_end
ret

Example 4 (by cb750mark)

Memory and I/O Bus for fCPU