How can I find the centre of a round table?
I think this technique using chords with 90 degree lines is probably the easiest to do because it involves standard construction tools and can compensate for inprecise measurements.

You just need a square, a measuring tape and a straight edge. (A large enough carpenter's square is all of these in one tool)


Draw two arbitrary chords (lines across) anywhere on the circle. Note the chords don't have to be the same length or lined up to each other in any way.
Find the exact center of each line
Use a square to project a second line towards the center of the circle at exactly a 90 degree angle to the chord 
Where the projected lines overlap is the center


 


You can repeat with additional chords get the center more accurately (which can compensate for any deviation in finding the chord center or getting an exact 90 degree angle)