To make an underground base you need to dig straight down 10 or 20 or so blocks and then you need to make a room 10x10 and have doors to other rooms in that room the one on the right potion crafting area one on the left crafting area and then another floor down only by 5 blocks and then can be your furnace room then go down 5 blocks again bedroom (10x10 each floor except for the rooms they can be any size) then go down to bedrock that is where you will mine because mining near bedrock has a higher chance for finding diamonds and that is your under ground base if you have any suggestions put them in the comments thanks!