For the B737NG.
Very broadly speaking, and assuming the crew, aeroplane, airfield are approved, and the procedure is in the FMC.
1)Preflight requirements.
Before we commence an RNP/RNAV STAR we need
one of everything to be working.
For an RNP approach using LNAV only, one of everything
For an RNP approach using LNAV and VNAV, in addition to having one of everything, we need 2xADIRUs in NAV and 2xPFDs
For an RNP AR approach, down to a DA(H) we need two of everything, (except the EGPWS and Autopilot). We fly these as RF (curved approaches).
2)Contingencies procedures before and after the FAF.
Again very broadly speaking we should carry out a missed approach if..
After the IAF, and in IMC, any message that indicates uncertainty of position, when unable to engage/reengage LNAV, or LNAV/VNAV, if the approach is an LNAV/VNAV AR approach a DUAL RA failure.
After the FAF, using VNAV then we must carry out a missed approach if we have a continuous Vertical Deviation Alert.
Our manuals are more detailed but that's the gist of it.