The three important things are Matrix multiplication, transpose a Matrix and invert a Matrix. Look for Gaussian elimination for the inversion. I always used Excel too, to see graphically what kind of model I had to use (direct lineat, log-log, quadratic, et cetera.
Another way is to look up the formulas that involve terms line x, x^2, x*y, y^2 et cetera, no linear algebra required.
I have this method in my Matrix class: (it's in
java)