Okay, so if you’re a nut about physics, this is one I can sketch out fo you, but you’ll need to fill in the gaps on your own.  If you want an easier method, check out this post here.

You can recreate Galileo’s mountain-top experiment by arming yourself and a friend with identical digital watches and flashlights.  At a specified time, one of you flashes the light, and the other records the time when the flash is seen. The trouble with this is at unless you’re on different planets, you’re going to have a hard time seeing a less-than-instantaneous result.

You can modify this experiment so that you set up a mirror (instead of a friend) far away, and bounce a beam of light off the mirror and record the mound of time it takes for the light to travel the set distance.  And instead of using your eyeball to record “when” the flash of light returns, you can use a strip of film on a spinning wheel. A further step is to split the initial beam in two, and have one beam take a longer path to return home, and record the time difference on film (which you can back-calculate to get the time difference).

The first successful speed of light measurements were made by a Danish astronomer using an eclipse of Jupiter and Io.