This somewhat depends on the situation:

ALWAYS: Squawk 7600 on the transponder, and continue to transmit in case your radios still work outbound, you just can’t hear anything coming in. Don’t forget to troubleshoot – volume knob, intercom squelch, etc. Assuming you have a real radio failure and you are in an actual lost communication situation:

1) If you are in visual meteorological conditions (VMC), or if you encounter “good” VMC along the way, you should maintain VFR and land as soon as practical.

2) If you are in instrument meteorological conditions (IMC), you need to think about two things – ROUTE and ALTITUDE:

ROUTE:

• The route last assigned by ATC (or the route ATC has told you to expect in a further clearance)
• If you are being radar vectored, use a direct route from the point of radio failure to the fix, route,
  or airway specified in the vector clearance.
• If you have not been assigned or told to expect a route by ATC, then fly the route you filed in your IFR flight plan.

ALTITUDE:
Fly the highest of:

• ATC assigned altitude
• altitude ATC has advised you may expect in a further clearance
• minimum enroute altitude (MEA) for the route segment being flown

So that covers the enroute phase of the flight – what if you are in a hold (or have received a clearance limit) when the lost communication situation occurs?

Continue holding (or hold at the clearance limit), and leave the hold/clearance limit at the expect further clearance (EFC) time. You did get and make note of the EFC time, right? Adjust your last circuit of the holding pattern to arrive at the holding fix and be able to depart the hold as close to the EFC time as possible. If the hold was enroute, continue the flight using the above route and altitude procedures.

Fantastic. Now how do I know I am cleared for the approach in a lost communication situation?

ATC will expect that you will begin the approach at or after the estimated time of arrival (ETA) you filed on your flight plan (or as amended with ATC when you were still in communication with them). If you arrive at a fix to begin the approach before your filed ETA, hold as published on the approach procedure until the ETA – and again, plan to depart the hold (and begin the approach) as close to the ETA as possible.

If no hold is depicted on the approach chart, hold at the initial approach fix (IAF), AND MAINTAIN THE ENROUTE ALTITUDE until you are able to start the approach at your filed/amended ETA. Plan your descent and departure from the hold to begin the approach procedure as close as possible to the ETA. You may have received an expect approach clearance (EAC) time. If this is the case, use this time instead of your filed/amended ETA as the time to begin your approach.

RESOURCES:

• 14 CFR 91.185 – IFR operations: Two-way radio communications failure
• Aeronautical Information Manual (AIM) Chapter 6 Section 4: Two-way Radio Communications Failure