Just what I do.
Wash your baby in baby shampoo. Face and body. Then use any conditioner and lube up the matts. Cut the matts out of the arm pitts and belly and butt regions.
Get a good leave on doggie conditioner and take the time to brush the outside hair to a gorgeous shine, you will be glad you did. Invest in a good dematter, just like suggested above. It leaves the length but gets out the mats.
Cut the hair short around your puppies eyes to avoid irritation and goo.
Show their eyes......they will appreciate it.
Visiors are out anyways.
