Can someone provide me with a book or online reference on how to construct smoothing splines with cross-validation? I have a programming and undergraduate level mathematics background. I would also appreciate an overview of whether this is smoothing technique is a good one for smoothing data and whether there are any disadvantages of which a non-statistician needs to be aware.

*Nonparametric Regression and Spline Smoothing* by Eubank is a good book. You probably want to start with Chapters 2 and 5 which cover goodness of fit and the theory and construction of smoothing splines. I've heard good things about *Generalized Additive Models: An Introduction with R*, which might be better if you're looking for examples in R. For a quick introduction, a google search turns up a course on Nonparametric function estimation where you can peruse the slides and see examples in R.

The general problem with splines is overfitting your data, but this is where cross validation comes in.