The best place to look for information is Campbell and GPSA. I am sure that other books include the information. You mention TEG so I am assuming that you are going to contact the TEG and gas in a contactor column as opposed to using the TEG for hydrate inhibition during the cooling of the gas.
The regeneration will take place at atmospheric pressure. From the contactor tower the pressure is flashed to close to atmospheric.
Be careful if you are using HYSYS for the design because the equilibrium and thermodynamic data was wrong. This was going to be corrected but to date I have not had it confirmed that it has been.
The components of the regeneration system are (in order from rich glycol flow from the contator) Condenser coil at top of stil column, lean/rich glycol exchanger, flash drum, still column, reboiler vessel, surge section in reboiler or separate vessel, lean/rich HEX, pumps, glycol cooler (may not be needed) contactor column. You also need to add particle and 10% carbon filter, usually after the flash drum.
The condenser coil should be designed for 10 deg C rise in the glycol. The flash drum should operate at about 70 deg C
The glycol flowrate should between 2 and 5 US gals per lb H2O. Contactor tray efficieny of 25%. Temp diff between dry gas and lean TEG 5 degC
You also need to consider the dewpoint that you wish to achieve and the corresponding TEG concentration that is needed. You may need to add enhanced regeneration methods stripping gas or Drizo. There is also Cold Finger but in my experience does not work, but thats another story.