Charlemagne's descendant? So they say...

I've heard before that many people (especially if they are European) are descended from Charlemagne. Many are supposedly descended from British royalty, too. I was having a look at the Wikipedia page on the genealogical relationships of Presidents of the United States and marvelling at how many of them are related to each other... and to the British royals. Barack Obama and George W. Bush are tenth cousins? Wouldn't that make for an awkward extended-family reunion!

What boggles my mind, though, is how all of this was determined. Finding out about your tenth cousins requires going back quite a ways... probably about 300 years. My question is this: how on earth do they do that?

I've been researching my family tree for years (probably at least 10, at this point), and I've yet to come across anyone who even comes close to tying into a royal tree. Most of my ancestors were farmers, fishermen, labourers, or servants. I'm always on the lookout for that one person from long ago who can help me break into the royal trees... but so far, no luck. The brick walls at approximately 1800 in various branches of my tree don't help, either.

Mathematically speaking, there is probably some blue blood in the family tree; I just have no idea how to find it when the last two hundred years have been obscured by my family's less-than-royal pedigree. Poor folks didn't always keep the best records...