Much of the procedural elements of the IFR rating involve dealing with radio communications failure. If we could completely count on radio contact, then such things as initial clearances, procedure turns, and even expected arrival times would be largely unnecessary, because we could simply expect ATC to give vectors to final and keep aircraft separate in real time.
If you experience a radio failure, put the code 7600 on your transponder. If you can still hear ATC (but not transmit), keep listening for instructions. (A standard procedure for ATC is to ask if you can hear them and have you IDENT in reply. Other questions can also be answered with an IDENT.) If radio reception is also a problem, listen over nearby VOR and NDB channels, which ATC will also try.
The procedures for two-way radio communications are covered entirely by FAR 91.185, and, of course, here:
I. VFR: If communications failure happens in VMC, or if VFR conditions are encountered after the failure and you can stay in VMC, you should continue the flight under VFR and land as soon as practicable.
II. IFR: If the failure occurs in IFR conditions, then you should continue your flight, and ATC will also assume that you are continuing, and clear airspace accordingly. The three elements of the navigation are:
Think of "Avenue F": AVE F. This is the order of priority to your routing:
1. Assigned: Fly the route assigned in the last ATC clearance
2. Vectored: If being radar vectored, fly directly to the fix, route, or airway specified in the vectoring clearance.
3. Expected: In the absence of an assigned route, fly the route that ATC told you to expect (in a further clearance).
4. Filed: In the absence of an assigned or expected routing, fly what you filed in your flight plan.
Fly the highest of these three, for the segment of flight you're on:
Assigned: The altitude assigned in your last clearance.
Expected: The altitude that ATC has told you to expect. ("Cherokee 2RJ expect 7,000 in ten minutes.")
MEA: The minimum enroute altitude for the segment you are on, as given on the enroute chart.
In flying the highest of these three, your altitude may change repeatedly, because the altitude assigned may be lower than the MEA for certain segments. In this case, you should climb to the higher MEA, and then descend again when the MEA is lower than your assigned or expected altitude.
Plan to leave the clearance limit or the IAF (if the limit was the airport itself) at the time calculated from your flight plan. On the plan was an expected time enroute: add that to your departure time off, and start your instrument approach procedure at that time. If you arrive at the clearance limit before then, hold there until that expected arrival time.