Wolverine is the guru of gore—expert at both pulling out the viscera of his enemies and witnessing his own internal organs on the outside. His mutant healing factor is no secret, but he’s learned to be an excellent actor, hiding the pain he has to endure before all that tissue regrows.
His rapid healing means he doesn’t need to worry about battlefield injuries, but Wolverine can’t spend precious minutes screaming in agony from all the bullets he sponges with his body. So he developed a useful secret. Logan masks the pain better than anyone.
He can’t conceal the fact that he bleeds out gallons if disemboweled. But in order to not panic his fellow X-Men and partners, he keeps his cool when covered in his own blood. This involves an intense internal focus so as not to freak out when he gets rend limb from limb or charred down to the (metallic) bone. Wolverine’s healing factor has been tested to the absolute limit and the mutton chop-sporting Canadian almost always bounces back from injury. He has regrown himself after being reduced to a single cell and survived from an atomic blast. He surely keeps a few extra yellow jumpsuits in his motorcycle in case he is blown to smithereens; and he has some handy mental tricks to deal with the pain associated with these incidents.
But the damaging effects of injuries have a long-lasting impact. In X-Men: Unlimited #12, by Stuart Moore and C.P. Smith, Wolverine explains he can feel phantom pain from serious injuries he recovered from months after they occurred. With all the battles he’s been through the stocky Canuck must feel perpetual phantom pains. But he has developed remarkable coping mechanisms to deal with the surplus of pain he shouldereds. One handy trademark of his ability is he recovers from mental trauma by a sort of healing mind wipe where all the bad memories disappear thanks to his healing factor. So some of the awful things he has done (because he’s the best at what he does) or were done to him, are erased.
To combat the physical pain of, say, having his arm ripped off or the Hulk divorcing Wolverine’s torso from his legs, Wolverine picked up some holistic pain-management techniques during his travels around the world. In the same issue mentioned above, he says he learned from a Japanese sensei to familiarize his pain, visualizing it as a physical being (like a mean, faceless monster). Then there's advice he got from a Tibetan monk to conjure up a caregiving angel—obviously Jean Grey—to protect him from the pain.
All these mental tricks keep him from ing out from shock, aided by his rapid healing, which prevents his nervous system from collapsing due to all the trauma he endures. This doesn’t mean Wolverine feels pain differently than a regular human; he still has to deal with all the sharp mental signals telling his entire nervous system to get away from whatever pointy object is doing him damage. But to save face—and look like the badass he is—Wolverine had to teach himself some tricks to disguise the pain. He uses a mantra to bear through it until the endorphins kick in. In his own words: “You don’t have to live through this ‘til it’s over. You just have to live ‘til the next moment. You’ll deal with that one when it comes."