As a layperson, I understand electromagnetic radiation to be a wave of photons with a certain frequency,
According to the classical picture, which is good enough for 90% of the engineering applications, electromagnetic radiation is a wave of oscillating electric and magnetic fields. Photons, on the other hand, are considered as particles and used to explain certain phenomena where classical picture fails. This is all about particle-wave duality and not many people can understand it fully. One can safely accept it as it is.
and different frequencies have different characteristics to us. For example, we can detect with our eyes certain frequencies, but others we cannot, even if they can cause otherwise visible effects (such as heating something up).
Yes, this is right. One can look at the electromagnetic spectrum to see the naming convention for electromagnetic waves with different frequencies.
A magnetic field, however, I imagine as something like a "force field" that attracts or repels things, which we can fluctuate to do work such as spin a rotor.
Well, you can consider an electric field as a force field, too. A positive charge creates a field around it and attracts negative charges and vice versa.
The key point maybe that when we think about electric and magnetic phenomena we think about static events, that is, there is a permanent magnet (or charge) I bring another permanent magnet (or charge) close by and they either repel or attract. Electromagnetic radiation is a dynamic thing. It is all about changing electric and magnetic fields as opposed to static ones.
I believe the two are related, but how? What does a wave of photons have to do with attracting things? I am looking at some practical, visual example of their relationship, if possible.
I think the phrase "wave of photons" is not quite right as I tried to explain above. Photons are particles to represent electromagnetic radiation. They have momentum and energy just like other particles.
Here is another example that might further demonstrate my confusion: crystal radios are powered by radio waves. Radio waves are often referred to as electromagnetic radiation that is at a low enough frequency that we cannot see it. I can imagine how a fluctuating magnetic field could power a radio and produce sound, but I can't picture how electromagnetic radiation could.
I think my above explanations answer this question but I can summarise with some quotations and an image from wikipedia page:
"Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum... Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with any charged particles."