You need three ingredients for a rainbow: light, raindrops and yourself. Every rainbow is literally in the eye of the beholder and even if you take just a pace left or right you will see a different set of raindrops reflecting the sun's rays back at you.
Rainbows appear when we have our backs to the sun, the sunlight shines over our shoulders and gets reflected in the raindrops of a passing shower.
At a certain angle the light will enter the raindrop, get refracted (or bent), split into the colours of the spectrum, bounce off the back of the raindrop and travel to our eyes. This causes a single or primary rainbow.
Occasionally you may be lucky enough to spot a double rainbow. These are caused by the light bouncing twice inside the raindrops. However some of the light will be lost by the second bounce so the secondary rainbow will always be fainter.
It will also be reversed with red at the bottom and violet at the top. In theory you could get multiple reflections causing multiple rainbows but in practice they are rare and very hard to see as they would be increasingly faint.
If you do get to spot a double rainbow, take a close look at the spaces around the rainbows and you might notice something interesting. The stripe between the rainbows will look darker than the surrounding areas. This is known as Alexander's Dark Band, named after Alexander of Aphrodisias who first described the effect in 200 AD. He didn't understand why this was the case but we now know it to be the fact that the light in this area is being reflected at angles that don't reach our eyes.
Unfortunately the only thing I don't know about rainbows is how to find the pot of gold at the end... I'll have to keep working on that one!