I'm aware of the existence of circadian clocks, but I don't understand exactly how circadian clocks regulate other circadian mechanisms. For example, if an enzyme is found to have a circadian rythm, how is this rhythm produced? Is it because of one or more clock genes?
Molecular feedback mechanisms create rhythmic patterns. The circadian rhythm is driven by a handful of genes, which in turn can regulate a number of downstream factors.
Here is a very nice explanation of the Drosophila circadian clock, which gives you an idea how this works. The video shows the same animation adding more factors every time to guide you through how the system works on the genetic/protein level.
A brief summary: The genes period and timeless are transcribed over night. Their proteins stabilize each other and build up in the cell. At the same time they block their own transcription, limiting the amount of proteins. Other factors destabilize the proteins and evoke their degradation. One of them is the light activated protein Cryptochrome. This helps entraining the clock and results in the removal of Period and Timeless protein during the day. The negative feedback of their blockage is removed and transcription starts anew at night, when Cryptochrome is inactive.
These clock genes do not only regulate themselves but can also activate or deactivate other factors resulting in daytime-dependent transcription of genes or protein activity.
The whole picture is of course a bit more complicated and involves a lot of additional factors. But also in humans and other mammals you find very similar mechanisms.