If you're going to be using a ricer, just halve the potatoes -- you can then put them cut side-down into the ricer, and then press -- the skin will be left behind.
(I'd still give them a quick scrub before boiling them, though).
Of course, this is easier, but not necessarily faster as it'll take longer for the potatoes to cook through.
If you bake them, just clean, bake, then cut in half, and put through the ricer.
(Again, not really that much faster).
If you're cooking red potatoes, even if you're not using a ricer, there's no need to peel them beforehand, as you can boil them whole, then rub the skin off with a dry towel.
(of course, for red potatoes, they're always going to be lumpy, and have texture, so in that case, I tend to leave the skins on).
To reduce the overall time, if I'm going to be going for a smooth mash: Only use large potatoes.
Save the smaller ones for applications where you don't need to peel potatoes.
Cut the potatoes into slabs.
There's no need to get them to cubes.
I tend to go to about 2cm (~3/4") thick.
Any extra cooking time is made up for by reduced cutting / transfering bits to the pot / dealing with the chunk that fell and rolled under the cabinet / etc.
Start the water warming while you're peeling.
You don't want to place the potatoes into boiling water, but you can take some of the chill off it.
Toss a few cloves of garlic (whole, but paper removed, end trimmed off) in with the potatoes, so you don't have to season afterwards.
Use stock rather than milk.
I keep boxed vegetable and chicken stocks at room temp, not chilled, so I don't have to heat it up first to deal with the issues of it cooling down the starches too fast.
Decide if the ricer's really worth it
-- I get good results just tossing everything back into the same pot after straining, hit 'em with a potato masher, add some liquid, then go through a few more times.
It saves a lot of cleanup, but it might not be exactly the texture you're used to,
cooking.stackexchange.com/users/67/Joe
I almost never peel my potatoes before boiling them for mashing.
So it's pretty much into the pot with some salt, cook, drain, and then mash with a standard masher.
A ricer does a lovely job
but it's a lot of work and mess.
That's pretty much a single pot, 30-45 minute solution
and I'm not sure it can get much faster or easier than that.
If you really want to use the ricer and loose the skins then try baking them rather tan boiling.
If you've already got the oven hot for a turkey, ham, or something else then putting the potatoes directly on the rack for an hour (ish) will get them cooked.
Then just scoop out the insides and mash.
cooking.stackexchange.com/users/2094/Eric Goodwin
Tools
Those little palm peelers work great for me - your mileage may vary.
If you have an apple peeler/slicer/corer , you can use this for potatoes as well, so long as they're fairly uniform.
The spiral-cut potatoes will cook faster too, but may also absorb more water - if you're worried, just move the blade out of the way and use the device only to peel.
Techniques
If you boil the potatoes skin-on the day before and refrigerate overnight, the peels should slip off the cold potatoes easily.
Then re-heat by simmering in your liquid, and rice or mash.
If you're really after quick, accept dirty results: as both Eric and Joe suggest, don't bother peeling and just toss everything together in one pot.
He suggests a masher, but a stick blender or hand mixer can speed this up even more.
cooking.stackexchange.com/users/86/Shog9
I NEVER peel potatoes except when making French fries.
What a waste of time!
I just scrub and boil 'em for 40 minutes.
The skins slip off like a charm.
Why on earth would you want to go through all the work of peeling?
If you're doing something where the shape is important, like potato salad, shorten the boiling time by about ten minutes.
I was really ticked during a recent visit when I offered to prep potatoes for my hostess and was told to peel about 50 or so of the small spuds; they were not new potatoes, but the same size.
So I spent a good hour doing that.
Then they took off minor blemishes and boiled them for mashed potatoes.
My opinion is that all that could be done when the potatoes are boiled, soft and amenable.
cooking.stackexchange.com/users/5937/sprout
Wash, cut in half, pressure cook 10 to 12 min.
Rice, add whatever you like.
I use a little butter, milk, garllic, salt, Pepper, whisk with fork.
Done in about 20 min.
cooking.stackexchange.com/users/40741/Dick
Microwaving is clearly the fastest and easiest way, no contest.
Rinse potato (30 sec).
Wrap in wet paper towel and put on plate (30 sec).
Put in microwave for about 2-5 minutes and make sure it is nice and soft.
Cut into pieces then mash with a fork and mix with whatever you like for flavor (1-2 min).
Total time to prepare is about 4-8 minutes, depending on the amount of potato you need.
I do this twice every day, works great.
Doesn't taste quite as good, but it certainly tastes good enough for me to eat twice every day, and great for those of you who don't feel like taking an hour to prepare your food.
cooking.stackexchange.com/users/20326/Brian
I've always thought that mashed potatoes should be a really simple thing to make.  But I find that with all the peeling, quartering, boiling, not to mention the incredibly messy cleanup, it's actually quite an arduous and tedious process.  Assuming I plan to use a ricer to actually do the mashing, is there any faster or at least less messy way to soften the potatoes than boiling them?  Any shortcuts I can use?
What is the fastest/easiest way to prepare potatoes for mashing?
cooking.stackexchange.com
<potatoes>
cooking.stackexchange.com/questions/7191
cooking.stackexchange.com/users/41/Aaronut
You can leave the skin on and halve the potatoes, as the ricer will leave the skins when the rest of the potato is pushed through. You can also save time by only using large potatoes, start the water warming while preparing the potatoes and use the same pot for mashing as you did for cooking. You can peel the potatoes after boiling to save time. It is also often easiest to mash them in the pan that put them through a ricer.
Cut the potatoes in half and put them through the ricer cut-side down. The peels will stay at the top. If you use large potatoes then you have less work to do. Warm the water while peeling. You can use the same pan to mash in after. You don't need to peel them before cooking and they will be easier to peel after. Cooking in the microwave is much faster than boiling.