Two things need doing in the first two days, in this order: make sure the doors cannot close on you, then close them on anyone who should no longer hold a key. Everything else, including deciding what to do about IT in general, can wait until the following week, and deciding it in a panic is how companies sign three-year contracts they regret.
If the departure is friendly, the leaver is your best source for the next 48 hours, and a short paid handover with a written list beats anything below. If it is not friendly, do the steps below first and ask questions afterwards.