How can you find a least square trend in a equation?

When given a set of data where the independent variable is time, it is possible to use statistical techniques to find a line (or curve) of best fit. One of the ways to do this is to minimise the square of the the differences between the actual values which are observed and the values that are predicted by such a curve (fitted values). The slope of this line or of the tangent to the curve at any point, is the least squares trend.

A statistical explanation of the theory or the calculations required are too much for the pathetic browser that we are required to use.