Re: How does one determine the half life of uranium-238 from scratch?

This is done experimentally.  There is not magic equation you can plug 
information into and produce a resulting halflife.

The methods are typically observations made through a scientific study of 
some sort that followed the decay of a nuclide over time.  It could also 
involve the use of mass spectographic analysis of the element(s) in 
question and/or their progeny.

if you look up a nuclides half-life you will find several usually listed 
for each nuclide as different investigations have yielded slightly 
different values.