I would perhaps suggest taking a look at the "Algorithmic Game Theory" book by Noam Nisan et. al., which briefly discusses this problem. The solution however, is left up to the reader.
If you're needing to actually compute correlated equilibria, and your input is a payoff matrix, I would suggest formulating it as an LP and then applying a standard LP solver like CPLEX or Gurobi. To formulate it as an LP, you introduce a variable for each cell in the payoff matrix, and constrain their sum to one. Then, for each player, action, and action the player can deviate to, you introduce a constraint requiring the deviation to have no better utility, conditioned on the probability distribution induced by the choice of action revealed to the player. This constraint is linear, and I would suggest taking a look at page 14-15 in the Algorithmic Game Theory book for an explanation of the constraint.
If your input is not the payoff matrix, you might still be in luck. For another good paper on (exact) computation of correlated equilibria in compact games, check out "Polynomial-time Computation of Exact Correlated Equilibrium in Compact Games" by Albert Xin Jiang et. al. (Edit: See Albert's answer to this question: Algorithms for Nash equilibrium computation.)