This is typically done with a "confusion matrix" which is a table of N classes by N classes that shows you what class a sample got classified as, versus what it's "True" class is. Ideal classification would yield a confusion matrix with numbers only along the diagonal. The more off-diagonal it becomes, the less accurate your classification algorithm is.
You can also use ROC curves http://en.wikipedia.org/wiki/Receiver_operating_characteristic which is a plot of true positives vs. false negatives. ROC curves are especially used in clinical studies.
