How is an Army unit stood up?

The CSA will decide based on recommendations from the field, the DA G3 based on a DOTLOMPF validated need (usually from the COCOM level), the branch proponent doing the leg work for the DOTLOMPF (reoccurring Gap Analysis) , the G5 strength potentially identifying bill payers for people-G3/4 identifying equipment donors. This wildly summarized (years long) process ends with an MTOE/TDA published by USAFMSA and an FY (E date) to be effective. DA G3 will identify a unit lineage from an order of merit list maintained by the TIOH. Streamers, colors, guidons etc should be ordered, but will likely be overlooked until 60 days out when a snarky staff officer identifies the shortfall (experience based sarcasm). A HQDA EXORD will be issued to the gaining MACOM with the E-date. The gaining command and HRC will start routing the personnel there within 12 months of the E Date. The booger gets flicked on the MACOM to stand it up. Equipment will trickle into the MACOM PBO/G4 channels and start to be fenced until the property book can be established. The month of the E Date, the unit will report C5 on the USR, likely with an internal USR done 2-3 months out from the E Date. Somewhere in there they will end up on a deployment order (sarcasm) with in 6 months of the E Date.

I probably missed a bunch, but that is what I have seen. The concept pings back and forth between the proponent, the G357, and the field to get the mission and the MTOE as right as they can get it before it sees the light of day with the CSA.

For light after dinner reading, you may also want to look at AR 220-1 and AR 220-5. The latter discusses activation, redesignation, and deactivation

It's not fun... LTC Jason Mackay gave you the run down, I was actually the first person assigned to a new company. The first day there was me, an empty barracks and a box of keys. I spent 2 days (as a SFC) taking the locks out of the doors and moving them around, just in case there were other sets of keys out there somewhere. I think it was the third day when I got the call that there were 32 new troops right out of AIT waiting at the rec center. I didn't have a clerk, any blank meal cards, I didn't have beds, blankets, or even wall lockers. In fact i didn't even have a supply Sergeant or even a typewriter.... Such memories.....

I don't know what the mechanisms are behind the scenes for standing up a unit, but having experienced it, its an interesting process to watch unfold around you.