I just use conditioner neat out of the bottle. Quick, cheap and easy! ;D There are some specialist products but I had no use for them.
Most matts can be teased out if they haven’t been put in warm water and felted. In the same way that putting a wool jumper in warm water will make it shrink, that’s exactly what happens when dogs with ungroomed undercoat are bather without grooming by their well meaning owners! ::)
I certainly don’t agree with the bit about “cut the hair between the mat and the skin.” I would always cut from the skin to the end of the matt, outwards, so that I didn’t make a hole in the coat. 😉