Some background info:
You may want to start by studying perceptrons and the learning algorithm (a building block for SVMs). It may also be useful to read up a bit on kernel methods (dealing with high dimensional data) in machine learning and Lagrange multipliers and how to apply them in different optimization tasks.
For understanding the theory:
There is a really good tutorial on SVMs which goes through (at least briefly) a lot of the background material and gives a good intro to SVMs.
"Pattern Recognition" by S. Theodoridis and K. Koutroumbas is a really good reference for SVMs and all of the theory behind a lot of pattern recognition related topics.
In practice:
Have a look at LibSVM and start playing around with some datasets from UC Irvine's machine learning data repository. Play around with different kernel functions and see how the classification accuracy changes under various conditions for different datasets.