Quite a detailed question in reality...aside of the preparation, materials and finishing which can differ depending on your needs/budget...to apply the design you first make a paint plan just like you used to get in an Airfix Model Kit...that paint plan is then used in various ways depending on the method of application you've chosen...
Either...to prepare basic decals which are then applied direct to the freshly painted and/or cleaned surface...its' the cheapest method and of course the decals will have to be replaced after 18 months or so...the material is just ordinary 3M type plastic/vinyl films and tends to eventually go off white after exposure to the sun...just as you could if signwriting a van or truck etc.
or...apply the design in paint using standard masking and spraying techniques...complex designs using a computer generated/paint mask
or...the expensive transfer/decal technique which BA uses for the tails of the aircraft and the red tick logo...lasts much longer than the cheaper version mentioned above...this is particular used where you have a large variation of colour graduation texture over a small area...you just cannot achieve that using a spray gun...for example the new Aeroflot tail has over 200 different graduations/variations of 4 colours on it so I am told
or...a combination of all 3 (or at least last 2 methods)...inevitably smaller details such as registration, 'cut here' signage etc. are done using the decal technique these days
All made almost simple/straightforward by the advent of the computer which 'shrinks to fit' so to speak