UPDATE: Some excellent additional suggestions and commentary over at Metafilter.
I believe it's pretty well established that I like to find the path of least resistance for a given task. Shoeshines are no exception. The real question is whether shining shoes is even worth doing in the first place. I think it is. Not if you're wearing Vans to work every day, of course. But if you've got occasion to wear a decent pair of leather dress shoes, you're probably going to need to shine 'em up once in a while. There are some pretty good shoeshine tutorials out on the web--I like this one. However, most people say that it'll take 30 minutes to shine the shoes. That's unacceptable if you're late getting out the door and you look down and notice that the shoes are ratty. I've got my shine down to under 5 minutes, which includes both shoes. Admitedly, it's not exactly a premium shine, but it fakes it pretty well and it'll last several days. Now, just to be clear, I'm utterly clueless about shining women's shoes. I'm guessing it needs to happen and that the process is pretty much the same. But I dunno. Standard disclaimers apply.
My dad taught me how to shine his shoes, back when I was knee-high to a
grasshopper. I know now that having your kids shine your shoes really is the path of least resistance! My son isn't old enough yet, but his day is coming... A few years after I learned how to shine shoes, I slapped together this little shoeshine kit holder box thingy in middle school woodshop. Dad is fortunate enough to not need to wear dress shoes anymore, so I get the funky kit. Here's what's in there:
- Some inexpensive liquid polish. This stuff has a foam applicator built-in, so you don't get your hands messy.
- Some decent paste polish, for when time isn't an issue.
- A horsehair applicator, for the times when I use paste (not often).
- A horsehair brush. Don't skimp on this, it's essential.
- Some soft chamois-type buffing cloths. I guess you could use an old tshirt if you had to.
The actual shoeshine process is super easy, but you'll add some time if your shoes are really manky. If you've been walking in the rain a bit, then you're probalby gonna have manky shoes. You'll need to take a minute to get the worst offenders off the leather. Water works fine, so does a dirty shirt. The dirty shirt method takes longer to get the stuff off your shoes, but the water method takes longer to dry. I generally go with the dirty shirt--I mean, you're gonna have to wash that shirt anyway, right?
So assuming you've got shoes that don't have tiny dirtclods hanging off them,
crack open your liquid polish in the appropriate color and start dabbing it around one of the shoes. If you start seeing foamy bubbles, you can stop squeezing the bottle and just spread the polish around. You really only need to worry about the toes and the heels. The middle part is tough to get shiny, so I usually throw some polish on there, but don't worry too much about it. Just be sure to get good coverage on the toe and heel areas. Now set that shoe aside to dry a bit and do the same thing to the other shoe.
When you've finished applying polish to the second shoe, go back to the first shoe and buff it all over with your horsehair brush. Doesn't matter if the polish isn't quite dry, just buff it all over until there aren't any wet spots of polish.
You can actually stop here with decent results. I usually take an extra 30 seconds to put on the final shine on the toes and heels, though. The way to get that final shine is to get your chamois cloth or clean tshirt 
and, with your foot in the shoe, hold onto the ends of the cloth and move it quickly from side to side while applying pressure to the shoe with the cloth. You'll quickly see the shine surfacing. Repeat on the second shoe and you're on your way.
