If you are talking about how they make the functions the mods do themselves, then that is a matter of many, many combines commands. Furniture most likely is from multiple invisible armor stands with blocks on their head. If you put 20/30/40 armorstands in the same place with different block on their head and different head/body orientations, you can basically make a block model without resource packs or actual mods.
Also, the way these creations work is most likely on a fill clock that is constantly powering a set of command (20 times a second) that check for you placing down a block or something, and doing stuff when that action occurs (like spawning in all those armor stands when you place down a certain spawn egg or block that creates the furniture).
But if you are talking about how they put all that stuff into one, two or three commands, then that is call a one-click command block structure spawner. These, when pasted into a command block on any world and powered, will replicate the command block structure the original creators made.
While there are many mcedit filters out there that will do this, the one that will copy the blocks in raw (not modify the structure or add anything) is GentleGiantJGC's mcedit filter.
If you would like to get started in making these types of things, i suggest looking through the Gamemode 4 modules. Gamemode 4 is a way to play MC with many of these modules installed in the world. They already have 35 modules, with things from undead players to extra hearts with heart canisters to using minecarts up and down walls. The most notable module is the custom crafter which is the universal way to craft special items that lots of other modules use to do their own special things and how to create a custom crafter recipe.