Hi! I did a little digging on this, and found a couple of excellent web sites you may be interested in:
http://eclipse99.nasa.gov...itions_morechina.htm
http://eclipse.gsfc.nasa....story/SEhistory.html
The Chinese were probably the earliest, with mention of elipse going back to > 2000 BC. In terms of a clear record of a date (that can be verified by checking to see that indeed there was an eclipse then!), it looks like May 3 1374 BC, again in China.
A total eclipse is not something folks would miss :-) So, mostly I guess it was a matter of having people with a good calendar and written records!
Cheers
Sarah