Analog Devices is one of the old-school companies - they've been around for a while and if you can dig through their website, you can find some real helpful documentation.
I'm hopeless on analogue stuff (A level in electronics years ago) and since then I'm purely digital, so I'm on a learning curve now! (I've just passed 40!)
Well you can't completely ignore analog stuff - sometimes a simple opamp can just make the project that much easier to do.
I've used variable resistor chips to adjust output voltage for a couple regulator chips, but the chips I used typically reference versus ground, which makes things much simpler. The pot. chips are only exposed to 1.25V which makes things much simpler.
To use the same approach with a 317 chip, the potentiometer chip's ground and the negative resistor terminal is connected to adj, it's power needs to be supplied from VIN(24V), using a simple shunt regulator (i.e. zener diode + current limiting resistor). The wiper pin is connected to VOUT. In order to convert the 0-5V serial signals from the PIC to the potentiometer chip, you'll need a NPN transistor and two resistors per pin that you need to translate up.
I think this approach is "doable", but it is going to be a couple of "features" you'll have to keep an eye out for:
1) The adjustment is going to be nonlinear. Resolution at the higher voltages is going to be pretty coarse, resolution at lower voltages is going to be pretty good.
2) The minimum voltage that the supply will output is ~1.2V
3) The typical resistance that the 317 wants is *very* low when talking about pot. chips. This won't matter as long as the PIC can adjust the final output voltage though.
4) The cheap variable resistor chips that I know of only have ~100 steps
I should mention that the method kchriste mentions - using an opamp to supply the reference current - the 317 only needs ~.1mA or so on the ADJ line, so there really shouldn't be anything difficult about that. The general idea is that the VOUT is always VADJ+1.25V, so just set VADJ to some voltage-1.25V and the 317 will do the rest.
James