Splines/Tridiagonal Matrices

[600burger]

I'm trying to find a spline for a set of points and solve it with a tridiagonal (at least thats what my prof wants). But...

1.)I'm unfamiliar with how splines work
2.)I don't see how a tridiagonal matrix will fit in
3.)what will the "Solution" look like? What will the solution of the tridiagonal kick out?

I have read the wolfram site and wikipedia as well as many other sites on the issue.

I really just need a general explanation of how splines are solved. I.E. not exact equations to find coefficients.

Thanks all!