First, you have to realize, that you normally will not see mats in your poodles' coat. He will probably look perfectly fine to you. If the hair is over and eighth inch long then there can be mats hiding in there.
You will need to have the correct comb and brush as just any type will not work effectively.
You need a slicker brush and a greyhound style comb. This is a comb with two different tooth widths and at least 6" long.
Begin by brushing your poodle with the slicker brush, doing the whole coat in sections.
This will pull out any loose hair. Then take the comb and go over each section bit by bit.
Mat removal is best done on a dry coat. As you find mats, use your comb to loosen them starting at the end of the hair and working up to the root. Do not start at the root as that will just tighten the mat up. There are sprays on the market that work wonders in loosening mats. I like Quicker Slicker by Nature's Specialties. You can find their website online. If you have a particularly stubborn or big mat, spray directly into it, getting it wet, and then start combing it out from the end of the hair up to the root.
After you have covered the whole body in this way take your comb and comb each area again to be sure you haven't missed anything. Then you can brush again with the slicker brush to get out any remaining loose hairs. Loose hairs are the pesky little things that create the mats.
Congratulations! Your poodle is now mat free!