Let me assume, you are a beginner in both assembler and DOS,
BUT you have installed things before and you basically  know
what a command line does and is used for.

Part 1: Set up a basic DOS system with FASM

(1)    Download  Dosbox  for  your platform from dosbox.com,
       install it and run it.  You should  see  the  command
       prompt coming up showing ’Z:\>’.  Hit Ctrl+F1 to open
       the Keymapper and hit ’Save’.  Close the mapper  with
       ESC, then close Dosbox with the command ’exit’.

(2)    You  will  need  to  find the configuration files for
       dosbox on your system.  It is in ~/.dosbox for  Linux
       and %LOCALAPPDATA%\DOSBox for Windows.

(2.1)    Create a directory where your DOS files will reside
         (e.g. ~/.dosbox/drive_c).

(2.2)    In ~/.dosbox replace the dosbox*.conf (current ver‐
         sion 0.74‐3) with this:

         [cpu]
         cycles=4000 # alleviate impact of busy waiting
         [sdl]
         mapperfile=mapper.map # see next sub step
         [autoexec]
         mount c ~/.dosbox/drive_c
         c: # change right away to our mounted drive folder

         Maybe  do a backup of the original, but you can al‐
         ways start over by just deleting the  configuration
         files and restarting Dosbox. ’Busy waiting’ may un‐
         necessarily heat up your  processor  and  eat  away
         your  laptop’s  battery, but it is normal with many
         DOS programs.  Look it up, if you have not heard of
         it before!

(2.3)    In  the same folder, rename the *.map file and call
         it mapper.map.  Then edit it: You will want to  re‐
         move most of the lines that start with ’hand_’.

         Dosbox  uses  most  function keys for itself.  This
         may have  surprising  effects,  e.g.  you  want  to
         compile  (only)  in fasmd (Ctrl+F9), but this combo
         is pre‐set to  kill  Dosbox!   Thus  it’s  wise  to
         delete these lines in mapper.map.

         Do NOT remove the line with ’hand_capmouse’ though!
         This will keep you from getting  your  cursor  back
         with  Ctrl+F10,  should Dosbox have captured it.  I
         actually rebound it to Ctrl+Esc with "key 27  mod1"
         to have the function keys clear.

(3)  Install  fasm for DOS from flatassembler.net.  Just un‐
     pack everything to ~/.dosbox/drive_c/fasm.

(4)  Start Dosbox. Your first FASM  session  may  look  like
     this:

     C:\>cd FASM
     C:\FASM>fasm
     flat assembler  version 1.73.31
     error: no 32‐bit DPMI services available.

     One  solution  is  to  get  the  HX  DOS‐Extender  from
     Japheth.  From the runtime you  only  need  to  extract
     said  DPMI  server  (hdpmi32.exe)  and place it in your
     drive_c folder. Execute this file before starting  fasm
     and you should see the program telling you it’s command
     line options, which means it works.

     Should you notice, that this magic only works once  and
     you  need  to execute hdpmi32.exe again after each fasm
     run, try running ’hdpmi32 /r’ :) As a  bonus,  you  can
     add  this  line  to your dosbox*.conf in the [autoexec]
     paragraph.

(5)  Start the FASM DOS IDE (fasmd.exe). Hit F4 and navigate
     to  EXAMPLES\COMDEMO and open comdemo.asm. You will see
     a simple ’Hello world!’ example.  Hit F9 to compile and
     run  it.  You  may  just see a short flicker, since the
     program terminates instantly.

     You can hit Alt+F5 to see the user  screen  (it  should
     show  the ’Hello world!’  message). You can, of course,
     also alter the code to your liking.  Without going into
     detail, insert the following just above ’int 20h’:

     mov  ah,7
     int  21h

     Hit  F9!  Now you should have plenty of time to look at
     your program’s output.