Hmm, it seems this bores people :-/ Might as well finish it...
There are really two parts to this. Proving the Earth rotates is simple:
Marking a stick and leaving it to rest in a water bowl, or putting a pendulum in a bell jar (a la a Foucault Pendulum) will suffice for a personal observation of the Earth's rotation if you're at a sufficiently high lattitude. You can actually measure your current lattitude with a significantly accurate device - at 45 degrees here it's about ~10.5 degrees per hour. If you are at or near the equator, or don't want to mess with such equations, you will need to use a gyroscope (or any wheel, really) and orient it properly.
I actually used to write testing applications for ringlaser gyros. A few degrees per hour is a fairly significant change when flying a plane across a continent, and inertial measurement units need to be able to track and account for such motion. An exact enough measurement will give you the sidereal day (the 'rotation' of the celestial sphere), which is a bit shorter than the normal (solar) day. This difference amounts to about 3 minutes and 56 seconds - ie one rotation per year.
Anyway, the argument against heliocentrism was not a religious one, but a logical one. The Greeks had found, that if it were true, they could find [http://en.wikipedia.org/wiki/Parallax parallax] in stellar motion, while, in fact, the stars were fixed (to them). It's hard to fault them for this when they can't even see the closest star year round and it's still some odd 40 trillion kilometers away. People don't comprehend such distances easily, if at all.
But, this parallax exists, and shows, fairly clearly, that Earth is undergoing greater acceleration around the sun, than the sun is going around Earth. Other methods (like Lilac's) tend to merely make putting Earth at the center look absurd by comparison.