B737 first officer reported during cruise descent they got a low oil pressure indication on the number 1 engine. They ran the QRH and performed the engine shutdown procedures.

Narrative

I was the first officer from ZZZ1-ZZZ2. In a cruise descent at approximately 35000 feet;the lower Display Unit (DU) activated and displayed an amber oil pressure on Engine 1. The captain directed me to notify ATC. Shortly thereafter the oil pressure entered the red band and I performed the 'ENGINE LOW OIL PRESSURE' QRH procedure while the captain flew the aircraft. The captain seemed to be having a difficult time with the autopilot which complicated things. The captain then directed me to let ATC know we were diverting to ZZZ. I asked him about going to ZZZ3 which was slightly closer. After considering this he told me to let them know we were going to ZZZ3. After a few moments he asked me to ask the controller for weather at ZZZ3. The controller replied with something to the effect rain; windy and low ceilings. The captain then told me to tell ATC were going to ZZZ. The 'ENGINE LOW OIL PRESSURE' QRH procedure directed us to perform the 'ENGINE FAILURE or SHUTDOWN CHECKLIST'. This checklist was completed and it directed us to the 'One Engine Inoperative Landing' checklist. All while this was going on the captain was fighting with the autopilot to get the jet down. At some point he decided to just hand fly. Sometime in the descent the captain gave me the aircraft to talk to the flight attendants and the passengers and ACARS dispatch. We received deviations for weather (to the south) and set the aircraft up for a landing on RWY XX. At the conclusion of the deviation the captain then took back the aircraft. The controller then started vectoring us to the north which was confusing. The controller then told us this was vectors for RWY XY. At this point we were about 5000 feet and on downwind. I got back in the box and set it up for RWY XY and changed all freqs; courses and decision altitudes. We asked for delay vectors as were still somewhat behind on all checklists (Abnormal; and normal). ATC vectored us across the localizer and when we finished the before landing checklist to the line; we began the approach. The captain flew the approach and landed. Crash Fire Rescue (CFR) approached the aircraft on the runway but ATC told us they couldn't comeup on the tower frequency so switch to ground. We did and asked CFR to check the left engine and brakes. I asked to check the brakes because the captain; upon touchdown; used max manual braking. CFR said all looked normal and we received taxi instructions. Upon reaching the ramp we waited for over one hour for the station to get personnel and park us. Reflecting back; in the cockpit; for me; it was pure chaos. While the captain was flying and trying to get the autopilot worked out I was running checklists; talking to ATC; manipulating the Mode Control Panel (MCP); and trying to be a 'Pilot Monitoring'. We don't train for this scenario. I could not have wished for a better captain to be with through everything. He created a calm environment and made sure all aspects of the flight were dealt with kindness; courtesy and professionalism aside from his tremendous Knowledge and skill. Unfortunately; this was his last flight due to retirement. I wish for him it was less memorable. As for me; I still have many years to go. For my own knowledge and experience; I request a crew debrief with the FOQA.Cause: It is my belief that we did what the situation required to operate at the highest level of safety. I'm sure there are things that could have been accomplished better.