Let's say I have a very small device, like an RC airplane, which transmits information as well as receiving commands for control. The body is made out of non-conductive foam, therefore not much ground is available. How can quality transmissions be achieved with very little ground available?
"Ground" is not the same thing as "Earth". It may be confusing because the surface of the Earth is sometimes called "the ground", but still this is an entirely different thing than electrical "ground". It is often convenient to define ground to be Earth, but that's no requirement. In a battery powered system far away from Earth, "ground" is likely the negative terminal of the battery.
You may be confused because monopole antennas require a good "ground" to function. To amateurs the most familiar monopole antenna is the common vertical.
However, the "ground" need not be Earth. It can simply be some elevated conductive wires or tubes:
Here, the three sloping tubes are the "ground". Drooping them results in a better match to 50Ω coax.
There are of course many antenna designs besides monopole antennas. Here are just a few, none of which require any special ground to operate: