Hi,
this answer comes a bit late, but I wish someone still finds this information usefull.
Lipschits constant is defined as
From the mean value theoream one can see that
so at every point if the constant Lis greater or equal than the norm of the functions derivative, then L is the Lipschitz constant.
The procedure to find the Lipschitz constant is to calculate the derivative of the function and then check if the derivative function is bounded by some value L on the domain - - that is your Lipschits constant.
Usually the norm is the euclidean-norm 
You can do the calculations with symbolic toolbox
syms x
f = sin(x); % here we define the function
df = diff(f) % here we calculate the derivative function of sin(x)
df = abs(df) % here we use the euclidean norm
fplot(df) % plots the abs(df). The function is clearly limited with upper bound M=1
% so the Lipschits constant is L >= 1
