As lescef has said, initially I'd be tempted to do it thusly:
1 By hand, teasing out as much as you can before resorting to cutting. Less stress for the dog. Have a look on Amazon (or Google) for Wahl spray detangler/conditioner - it's good stuff and will help lubricate (smells nice, too).
2 Then a combination of a wide toothed steel comb and sharp scissors (blunt ended) followed by
3 A mat breaker as a last resort. I'd avoid the cheap multi-blade mat breakers as the blades aren't sharp enough to avoid pulling. I have one of these if the worst comes to the worst and can recommend. Reversible and spare blades are available:
http://www.diamondedgeltd.com/show-tech-mat-buster-coarse-c2x22347619 Go gently. Try not to pull but let the blades do the work.
4 Best tool is patience. Don't go mad!