This is a classic calculation of a decay constant.
We consider an allowed Fermi transition (so we do not consider angular
momentum changes). The calculation will be done for ordinary 
decay; the modifications for 
decay are trivial. Electron
capture is treated separately (well, is left as an exercise).
The decay constant 
is given by Fermi's Golden Rule
(Number 2):
where 
. Thus we need to caclulate (i) a matrix
element which couples the initial and final states, and (ii) a phase
space factor which describes the volume of phase space available for the
outgoing leptons. Note that we need to use relativistic mechanics, as
the (anti)neutrino is always relativistic, and usually 
.