One way I explain it is from a physics perspective which for some people is over their head but if you can get them to visualize it helps. An altimeter is a measure of the amount of air molecules. Obviously the lower you are the more air molecules there are.
Pressure (static pressure) being the force those molecules exert when they are not moving. In other words if I take the student's hand place a book on it, then I am increasing the "pressure" by placing another book on top of his hand. Or if you can explain a manometer (just a U-shaped tube with one end closed) and why we use "inches" that works really well too.
As the the pressure increases, as in when you fly lower, decreasing your altitude, the static pressure of the air pushes the liquid (mercury, Hg) at Pa down. This by the way is what a static port measures. The higher the pressure the farther the mercury gets pushed (H) and that is why 30.92 inches Hg is a higher pressure than 29.92 inHg. This is the length in inches from the opening of the tube. In other words a lower altitude. If I set the altimeter on 0 and watch as the altimeter setting from the ATIS increases then the altimeter will indicate a negative altitude. Specifically about 1,000' for every inch of Hg. We all know this the question is whether or not we understand that and can get a student to understand that.
So when I say pressure altitude is the altimeter corrected for non standard pressure, I mean I'm trying to find the difference in altitude as if the altimeter is 29.92inHg. Why? so we can have a reference point when we throw temperature into the mix to calculate density altitude.
Remember temperature is a measure of molecule's kinetic energy. If I say your kid or brother or whoever is really hyperactive and is bouncing off the walls then they have a lot of kinetic energy, therefore a high temperature. If I decide I need to fill an auditorium full of kids, I can fit a lot more of them if they are calm and not moving around. If those kids were air molecules then they would be "cold air."
However, if those kids are really hyperactive and running around, I would not be about to get as many of them into the auditorium and therefore they will not be as densely packed. If they were air molecules then they would be "hot air," and therefore not be as dense, as in less of them, as in they would indicate a higher altitude. This would mean less air molecules to produce lift, be used for combustion, etc meaning worse performance.
Therefore density altitude is the altimeter corrected for non-standard temperature. Increase the temperature above standard, decrease the density, and therefore you will have a higher density altitude, less air molecules. Standard temp being 15C at sea level, 13 at 1000,' 11 at 2000' etc; 2C per 1000.'
Now after all that you can explain some of the other factors that affect density. i.e humidity (less air molecules, less performance, especially means less air to expand during combustion), and high elevation; less air molecules, less lift and performance, who knew?
Anyway, hope this helps, if you can get a student to visualize this then they will learn it.