Information is coded into electromagnetic radiation (EMR) via slight changes in two basic properties of EMR: intensity and frequency (or wavelength or photon energy).
This works best when the frequency content of the information is lower than the primary frequency of the EMR being modified (the carrier). But there are fancy ways to encode low frequency radiation (say around 35 Hz) with higher frequency information. I won't get into those details.
This encoding can be analog, such as AM and FM radio and "old" TV signals, or digital as in HD radio and TV.
Analog encoding via intensity changes is called amplitude modulation (AM). The carrier EMR with no information would have a constant intensity: in a wave perspective, the amplitude of the wave is constant. in a photon perspective the # of photons per second is constant. Information would cause increases and decreases in the EMR intensity with (usually) a linear correlation between the info amplitude and the EMR amplitude/photon rate. The frequency of the EMR does not change but additional (much lower) frequencies are added matching the frequencies of the information.
Analog frequency encoding or frequency modulation (FM), the carrier with no information has a constant frequency. Information causes the frequency to vary around the carrier frequency with the amount of variation depending on the intensity of the information, and the rate of the variation (slope of the frequency change) being proportional to the frequency content of the information. (I might have gotten the amount and slope factors backwards, but those are the two factors that are changed). The intensity of the EMR does not change.
Digital encoding uses a variety of methods. Frequency shift keying (FSK) uses changes in frequency (two distinct frequencies) to show binary digits (bits), or changes in binary digits. Amplitude keying uses changes in amplitude to show bits on a fixed time scale (or changes in bits). Phase shifting can also be used for bits, but it is fairly noisy.
All of these happen at the rate at which the information is changing, but the carrier EMR carries it from point A to point B at speed c. Imagine a turtle being carried on an airplane. Even while traveling on the plane, it doesn't crawl any faster relative to the plane, but would get to a destination much quicker. Once it reaches the destination, it's still crawling slowly. Or imagine a thundercloud over a friend's house 1.6 km away, while you are talking on the phone to that friend. There is a lightning flash and a clap of thunder. Over the phone you almost immediately hear the thunder. About 5 seconds later you hear the thunder in the air. The information over the phone traveled at nearly c from phone to phone, but then became sound. The actual sound traveled at 340 m/s through the air.