When you say that the examples don't work, which ones don't work? When I go to the Documentation Center for DirichletDistribution the examples all seem to work as advertised.
Note that, for example,
DirichletDistribution[{1, 3, 2}]
is a symbolic representation of the DirichletDistribution at those values of its parameters. You need to then put it into, for example, PDF, to get its value at a particular point. So,
PDF[DirichletDistribution[{1, 3, 2}], {x, y}]
returns
Piecewise[{{60*(1 - x - y)*y^2, x > 0 && y > 0 && 1 - x - y > 0}}, 0]
And so on....
Read http://reference.wolfram.com/language/tutorial/ContinuousDistributions.html to get some more background on how to work with probability distributions in Mathematica.