What would be the proper FMC programming technique to divert to the closest airport (assuming autopilot, FMC and autothrottles work)? I have tried changing the ARR airport and selecting the appropriate rwy in DEP/ARR but the plane does not want to capture the approach. To make matters worse I usually do not have approach plates for the diversion airport. I am sure I must be doing this wrong, but so far have been unable to figure it out. A mini tutorial someone? Thanks in advance.

Go into the route page and change the destination to the new airport.In the route page enter your new route to your destination (with route identifiers), OR, just go into the legs page and type in the legs to your new destination. The DEP/ARR pahe will now reflect the new airport, select your approach, and away you go!

You could also enter the airport into the FIX page and immediate turn in HDG SEL direct to it while you program the FMC too...