Is there a special protocol for a situation where the on-board radio communication equipment suddenly breaks down? Would the pilot be able to land on a busy towered airfield or would they be forced to look for a small landing strip in the middle of nowhere?
It is important to remember that it is often difficult to diagnose radio malfunction during flight. Therefore it is hard to know whether you have a malfunctioning transmitter, a malfunctioning receiver, or perhaps both. You also have the point-of-failure that is the headset you are using. For this reason it is quite usual to carry a spare headset and the first piece of diagnostics is to swap headsets. Many General aviation aircraft also have a handheld microphone and speakers integrated into the radio stack.
Once you've ascertained that its the actual transmitter and/or receiver that has failed it is common to set the transponder to 7600. For landing, the relevant detail for the procedure to follow is contained within Chapter 4, Section 2-13 of the AIM:
Transmitter & Receiver inoperative
The light signals used for an aircraft in flight are as followssource:
Steady green - Cleared to land
They can be seen in this video.
First thing you do when the radio breaks down is to start squawking 7600 (the code for radio malfunction) on your transponder.
Then when you approach the airport they will attempt to contact you first through radio (to see if you can still hear them) and you use alternate means of replying (sending IDENT on transponder, rocking your wings,...).
If you can't hear them they will use a light gun to convey messages.
Ratchet Freak has a good answer. In addition, please pull out your cellphone and try calling the tower. Somewhere in the bottom of my flight bag I have a small book with telephone numbers at towers. If you don't have that, call Lock-Mart Flight Service at 1-800-wx-brief tell him you need the tower number.
Also remember that there is no requirement for a radio in an airplane. NORDO (No Radio) aircraft are perfectly legal although in practice, they operate mostly out of non-towered fields. Operating out of a towered airport is still possible, but it requires prior coordination with the tower. Note please that flight in the SFRA around Washington DC does require a radio, and I have seen no procedures to allow for NORDO aircraft in this area.
If your radio stops working, one option is to fly to a non-towered field and do what the NORDO planes do: Overfly the field at a safe altitude, note wind direction from the wind sock or tetrahedron, note other traffic in the area, and fit yourself into the traffic pattern... and land.
I was a Junior Technician, later Corporal, Air Wireless Fitter in the R.A.F. in 1952-4, servicing Gloster Meteors' radios at a Flying Training School, and the signal then was for the pilot to waggle the aircraft's wings as he approached, or flew by, on his way to land, to show he could not contact the Control Tower. Then we had to fix it.
I was made a Corporal so that I could sign off our work on the aircraft out on the airfield, usually just tuning up to a new crystal to suit the frequencies of a distant Station. I got the promotion so the Sergeant could stay in the nice warm office: I didn't mind -- I was "/Paid" extra, nice for a "National Service Only" erk.