Asian lady beetles have a wide range of colors and spot arrangements. Most are yellow, orange, or red with black spots or vice versa, but some have no spots at all. Look for the "W" or "M" markings on the top of their heads; this is their most recognizable feature.
Asian lady beetle
Asian lady beetles
Asian lady beetle nymphs

I remember a time when it was rare to see a lady beetle in the wild; this isn't the case anymore. Of course the beetles so prevalent today are not the friendly lady beetles (Coccinella septempunctata) I grew up with. They are a recently introduced species and similar in appearance, but are completely different in many important ways. The multicolored Asian lady beetle (Harmonia axyridis) has taken over the North American continent, including my house and yours. They have been somewhat beneficial for soybean farms and some other agriculture by controlling aphids, but they are nothing but annoying for the rest of us. Their terrible smell and propensity for flying into whatever you're drinking make these beetles a perfect target for immediate elimination.
Vacuum when you first notice the beetles congregating. One efficient way to control Asian lady beetle populations around your home is the vacuum method. If you can get them when they are forming into a big group on the south-facing walls of your house, you'll have the best chance of taking them out. What a lot of people suggest is inserting a knee-high nylon stocking into the end of your vacuum hose and securing the open end around the outside of the hose with a tight rubber band. This will serve as a collection bag within the hose, which you can tie off and dispose of as you see fit.
Wash the area to get rid of pheromones. Studies show that the beetles secrete several substances when they are grouped together. The substances (pheromones, feces) attract other lady beetles, and this is partly why these insects aggregate as they do. The staying power of those substances is why the beetles seem to keep coming back to the same spot year after year—that and seasonal solar alignment. After you've removed all of the beetles, wash the area thoroughly with soapy water and a brush, then rinse with a hose. If beetles come back, you may need to repeat the process with a more potent soap.
Make your walls and siding beetle-proof. The reason these beetles are so interested in over-wintering in the walls of our houses is that in their native environment on the Asian continent, they like south-facing, light-colored stone cliffs. Our (usually) light-colored houses, with their vertical arrangement and their nooks and crannies, are a most convenient surrogate. Changing your house color seems like a pretty drastic step just for beetle prevention, but if you're in the market, maybe try a darker color. Seal up any gaps in the siding and any spaces around doors or windows with caulk. Also, fill any beetle-sized cracks in your foundation while you're at it.
Cover any holes or vents to prevent beetle entry. Asian lady beetles will also try to get into your house through ventilation holes in the roof and along soffit areas. Most of these ports will have mesh built into them, but it might not be small enough to prevent entry. Once you have filled the obvious gaps, you should make sure that they aren't entering through the vents. If they are, you need to buy metal window screening and seal those vents up. It would be prettier to do this from the inside or with a trim nailer, but a staple gun will do the trick as well.
Make sure your windows have screens. Go ahead and put this advice on the "duh" pile if you want, but I'm serious here. Make sure your windows have screens, that those screens don't have holes in them, and that they are inserted and aligned within the window frame properly (no gaps around the edges). When it comes time for the Asian lady beetles to find an over-wintering location in the fall, they will be shimmying their way into any space they can find. The same goes for the space around the window frame and window trim. Caulk tightly on the inside and outside to prevent unwanted beetle entry. It also cuts down on drafts.
Trap as many beetles as you can. Once beetles have established themselves for a season, they become difficult to get rid of in one fell swoop. During warm stretches in winter, beetles will be coming out of the woodwork. Notice that they are attracted to a couple of things: your windows, and any source of light. Use this knowledge to your advantage. They bounce around in your windows because of the light outside, so place sticky traps in locations like windowsills, and you'll catch a fair number of them. Light based traps are another option at night. There is more on that in the right sidebar.
You might be tempted to grab the cat, set off a couple of bug bombs, and book a room at a local hotel for the night after the first time you wake up with one of these beetles in your mouth, but it won't really do any good. Sure you might kill a few beetles, but the great majority are going to be snug as a bug within the depths of your walls. All you will accomplish is to give your entire living space a coating of poison—and doesn't that sound nice? There is a time and a place for this sort of chemical warfare: The time is in the fall, just before the beetles start trying to invade your home (September‒October in Minnesota), and the place is around the south- and west-facing outer walls of your house. You should also try to include possible entry points: window frames, roof vents, and around foundations. Use a potent pyrethrin-based insecticide like Demand or Demon WP. With any luck, it will serve as a chemical barrier to the coming onslaught of Asian lady beetles.

Menthol and camphor repellent. Menthol, which is an extract of mint, and camphor, which an Asian evergreen extract, both have a strong smell. Studies have shown that the two substances have a repellent effect against Asian lady beetles for up to forty-eight hours when applied to an area upon which they would ordinarily congregate.

Homemade light trap. My favorite DIY Asian lady beetle light trap design comes from Ohio State University, and it involves a couple of milk jugs, two clear plastic transparencies, and a cheap clamping utility lamp with a sixty-watt bulb: