We may know the value of a function f at a set of points
x1, x2, ..., xN. How do we estimate the value of the function
at any point x*; how do we compute f(x*). This
can be achieved by finding a smooth curve that passes though the
points (x1, f(x1)), (x2, f(x2)), ... (xN, f(xN)). Alternatively,
the points may be joined in sebintervals of [x1,xN] by
* piecewise *. A third method is that of defining a
straight line (or a polynomial of low degree) that is the best fit to the
set of points.
Tutorial on Approximation

Polynomial Interpolation can be carried out using a method called Newton's Divided Difference Method.

Tutorial on Polynomial Interpolation
: Polynomial Interpolation - Spreadsheet Demonstration

Tutorial on Piecewise Polynomial Interpolation

Tutorial on Basis Functions