simplex algorithm

I've got my decision maths a level exam in a few weeks, and the main bit I'm worried about is the simplex algorithm. I've been told to 'add a multiple of the pivot eqn to the other equations to get the pivot column to equal 0'. Yet I really struggle working out the equations needed by trial and error. I was wondering if there was any method for doing this? (I'm sure I've found one somewhere, but I can't find it again no matter how hard I try). Any help really would be appreciated