How do You Keep Your Boots Dry ?

Try hand warmers in your liners. They reach 135F and have worked for me to keep the boots toasty on winter camping trips. Don't know how much drying they can provide if your boots are REALLY wet, but they have worked for me.
Of course, I hardly sweat.

Being a serious foot-sweater, I'm always keen to hear others' approaches.

I've had decent success with my current method of sleeping with the liners. Sometimes down by my feet, sometimes around my legs, and sometimes I'll curl up around them in my torso area (where the most heat is generated). This works well with Intuitions because they're not sponge-soaked. Rotating socks and drying them out each night (in your sleeping bag) compliments this method. Sleeping with the liners will also ensure that they're at least warm when you put them on in the morning, even if still wet.

I've tried the 'old school' plastic bag method aluded to above and it just left my feet totally pruned because the moisture couldn't escape my socks. I had the most success with this method on 1-night trips, where the second day I could just go with socks, no bags, and you only endure 1 day of wet feet in the vapor barrier. On trips with more nights/days, it became equally unpleasant to put bags on my feet each day and still end up with wet feet versus having wet liners.

I air mine out depending on sun, wind, time left till bed, etc. Then, if still damp, I sleep with my liners. Don't know if snowboard boots have removable liners. Might be too bulky to sleep with!

That's my approach. I find my feet are miserable in the morning, unless I pull the liners and stick them in my bag. I usually put them inside a plastic bag down by my knees. They don't dry out, but they're warm!

Vapor barrier liners work pretty well for this purpose. If you have only a very thin synthetic liner sock between you and the VBL, my experience (and my feet tend to sweat a LOT otherwise) is that the liner sock gets damp, but not sopping wet. Something about your sweat glands sensing when the vapor pressure reaches a certain point and they stop pumping out more moisture I think, but the gist is that the sheer liner sock takes no time to dry at the end of the day, and the boot liner will only get wet from snow/water coming in from outside of the boot, not from your sweat. Bread bags do work and are a classic piece of gear, but they also tend to ride down more than a decent VBL (which you can make yourself pretty easily if you have a sewing machine - just some coated ripstop, a little elastic to sew in around the ankle, and perhaps a lace to tighten the top around the cuff and you're good to go!).

On day tours at this time of year, I tend to take off my boots and pull out the liners on longer rest stops. The socks dry nicely when I leave them on my feet, and the liners will dry a bit if I'm in a warm/sunny enough spot. But for multi-day action, if I don't have a drying room at night, I'd use VBLs...

As an aside, a VBL can also be handy inside your sleeping bag on multi-day trips, especially if you're using down., and especially in the winter when there's zero hope of drying out your back while you eat breakfast. But IME, you really need to manage your temperature level carefully so you're not overheating inside a sleeping bag style VBL, or else you'll really not enjoy the clammy factor.

Vapor barrier liners work pretty well for this purpose.

+1 to VB socks, but I wear my VB sox (2mm neoprene) next to my skin (i.e., no liners). I've tried liners but they get soaking wet, so it's next to skin for me. I've toured with VB liners 100% of the time for my last 100+ touring days, and I cannot imagine doing a multi-day trip with anything else.

I guess I cannot fathom using a VB sock due to space limitations in my boots. I leave plenty of toe space to free wiggle, but the heel cup it pretty solid and around the foot med-slack when hiking, but not enough room for a 2mil sock. Like Jim said using an ultra-thin sock and VB sock would work, but I would think the excess material would be bothersome.
I was looking at the Integral Design VB sock. I've never tried a VB sock, so I may be blowing gas here, but just looking at the picture of them looks like there would be excess material, plus the elastic looks like it's in a spot that would bind in the boot (at least leave a cool pattern on the skin).
Looks like one would have to re-mold the boot liner to compensate for using that system.  ???

I see REI carries a Gore-Tex model of a sock that looks a lot more trim, but pricey at $60.
I would think that Event would make a great copy of that sock since it breathes so much better than Gore and keeps the water out. I may have to make my own pair to test it out and not be so narrow minded. 
But I guess releasing water vapors into the liner is what this topic was about and trying to avoid doing, so the Gore and EVent may not be the best options.