I know they use two-way radio, but is that the only communication pilots receive from air traffic controllers? Also, in general in class A airspace, how often do pilots hear from air traffic controllers?
VHF radio is one method. HF is used in oceanic areas, but it is in decline.
Data comms are also used, it's called CPDLC (Controller–pilot data link communications). The ATC sends a digital message to the pilot, and they respond the same way.
Too Much Static Noise (HF)
On long flights, the controller can grab the crew's attention by poking them using SELCAL. Too much static noise for a long time is tiring to listen to.
Most of the chatter is handing off the plane from one controller to another.
If there's bad weather en-route, the pilot will ask to deviate. That's another type of chatter.
Also climb, step-climb, and descent instructions.
Changes to route are also relayed.
When flying over areas not covered by radar, position reports are also provided by the crew and confirmed by the controllers.
Traffic separation instructions and traffic advisory information are also quite common.
A VHF or UHF radio.
Class A airspace operates under IFR, so pilots must be on a filed light plan, cleared by ATC and maintain two way communications with ATC at all times.
That and hand signals don't work too well at 33,000 feet.
VHF & UHF in domestic airspace, HF transoceanic. Digital communications Controller/Pilot Data Link (CPDLC) have been used over water for some time and are in the process of being implemented domestically as "Datacomm". Over water is satellite communications while domestic digital will be carried over ARINC/SITA cell phone type networks. Datacomm is being fielded for Clearance Delivery at large terminals first with en route communications to follow.
As far as the towers go, I think they may still have light guns for signaling aircraft that lack radios.