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Coloured dots and stripes - whats that all about?
When you're looking for new tyres, you'll often see some coloured dots on the tyre sidewall, and bands of colour in the tread. These are all here for a reason, but it's more for the tyre fitter than for your benefit.
The dots on the sidewall typically denote unformity and weight. It's impossible to manufacture a tyre which is perfectly balanced and perfectly manufactured in the belts. As a result, all tyres have a point on the tread which is lighter than the rest of the tyre - a thin spot if you like. It's fractional - you'd never notice it unless you used tyre manufacturing equipment to find it, but its there. When the tyre is manufactured, this point is found and a coloured dot is put on the sidewall of the tyre corresponding to the light spot. Typically this is a yellow dot (although some manufacturers use different colours just to confuse us) and is known as the weight mark. Typically the yellow dot should end up aligned to the valve stem on your wheel and tyre combo. This is because you can help minimize the amount of weight needed to balance the tyre and wheel combo by mounting the tire so that its light point is matched up with the wheel's heavy balance point. Every wheel has a valve stem which cannot be moved so that is considered to be the heavy balance point for the wheel. (Trivia side note : wheels also have light and heavy spots. Typically the lightest spot on the wheel is found during manufacture and the heavier valve stem is then located diametrically opposite that light spot to help balance the wheel out).
As well as not being able to manufacture perfectly weighted tyres, it's also nearly impossible to make a tyre which is perfectly circular. By perfectly circular, I mean down to some nauseating number of decimal places. Again, you'd be hard pushed to actually be able to tell that a tyre wasn't round without specialist equipment. Every tyre has a high and a low spot, the difference of which is called radial runout. Using sophisticated computer analysis, tyre manufacturers spin each tyre and look for the 'wobble' in the tyre at certain RPMs. It's all about harmonic frequency (you know - the frequency at which something vibrates, like the Tacoma Narrows bridge collapse). Where the first harmonic curve from the tyre wobble hits its high point, that's where the tyre's high spot is. Manufacturers typically mark this point with a red dot on the tyre sidewall, although again, some tyres have no marks, and others use different colours. This is called the uniformity mark. Correspondingly, most wheel rims are also not 100% circular, and will have a notch or a dimple stamped into the wheel rim somewhere indicating their low point. It makes sense then, that the high point of the tyre should be matched with the low point of the wheel rim to balance out the radial runout.

What if both dots are present?
Generally speaking, if you get a tyre with both a red and a yellow dot on it, it should be mounted according to the red dot - ie. the uniformity mark should line up with the dimple on the wheel rim, and the yellow mark should be ignored.