Calculate Local Sidereal Time I am trying to follow this guide and move to a programming language
but I have doubts.

What means the strings A, B and C in this manual? 
http://aastro.org/wp-content/uploads/2010/11/Calculation-of-Local-Sidereal-Time.pdf
A highly authoritative source is Explanatory Supplement to the Astronomical Almanac 3rd ed., Urban &amp; Seidelmann, 2013.

Chapter 1 gives the introductory explanations, without all the refinements if you want millisecond accuracy. Page 12 explains that

local sidreal time = Greenwich sidereal time + east longitude

(This book assumes the reader is able to convert between angle notation and time notation whenever necessary.)

If accuracy of 0.1 second is sufficient, the formulas given by the US Naval Observatory should do the job. Note that for subsecond accuracy you will have to determine UT1, which can be up to 0.9 second different from the commonly available UTC. You will have to look up the difference each time you do the calculation because the difference cannot be predicted more than about 6 months into the future.