Build a 2x4' base for the cabinets to sit on.
Assemble the Ikea boxes, place them on the 2x4' base and secure them to the wall.
Add 2x4' blocking between the cabinet boxes and the wall for your trim pieces.
Cut and attach trim to all exposed sides, including crown molding and baseboard.
Patch holes, paint, and attach doors (we had custom MDF doors made and painted them to match).