First they ripped up the old floors.
What was underneath:
Then they applied a leveling compound which had to dry for an hour or two.
While it was drying the one guy started cutting trim. Once dry they cut the floor in for the main kitchen area. That was day one. Day two they applied leveling compound behind the fridge, then cut out the areas for the pantry and under the fridge. I think they only glued it at the doorways for about 8 inchs into the room. Then trimmed it all in quarter round.
Shot of trim by the sliding door:
Close ups: