For the numerator of the fraction, I add up all the transfers to savings that I've made for the year, plus all employee and employer contributions to my 401k. For the denominator, I take my gross salary, add the employer contributions to my 401k, and subtract income and payroll taxes. Divide the numerator by the denominator. I don't consider monthly savings rate to be all that informative, but it's easy enough to divide the numerator and denominator by 12 prior to calculating the savings rate.
Takes about 5 minutes with a hand-held calculator.