The 
Mutt side quest is available immediately after finishing the Prologue. This quest mainly consists of running around the whole map, investigating clues and wolf packs. Instead, we provide a quick shortcut to run directly to Mutt's location.
Finishing this quest will unlock Mutt for you, along with the Houndmaster skill tree. Mutt is useful for attacking enemies and animals or to occasionally follow a trail during certain side quests.
Step 1: Progress the quest north of Bozhena's Hut
Check your Journal, under Mutt quest you likely have "Find out what happened to Mutt." as your next task with a location pointing northwest of 
Bozhena's Hut. This is the only location you actually need to visit before you can go directly for your dog.
Go to this marked spot and encounter a bandit looting the body. He isn't friendly and you'll face a dialogue choice. Best is to use Intimidation dialogue option to scare him off and he will simply run away, but you can also kill and loot him - his only good loot is a badge for Farkle.
Investigate the body and the deer corpse, which will add another location marker to your map - the quest says you should go to Bozhena's Hut.
The ordinary Mutt route
Now Mutt has finally appeared on the map and you can go directly to the final location. But if you follow the markers, it will take you around the whole map, clue by clue. The stops are:
- Bozhena at Bozhena's Hut, who needs help with Bad Blood side quest
- Gamekeeper Vostatek between Tachov and Vidlak Pond, who can help only after completing Lackey side quest
- Herdsman Siegfried in Kopanina north of Tachov, who needs help with
Sheep among Wolves task
All of these activities, quests and NPCs are fully available after the Mutt quest, it just serves to show you around the map.
Now back to the shortcut - For the shortest way, go directly to the next location marked on the map in the image below.
Step 2: Go directly to the Wolf Den
The Wolf Den, where you can find Mutt after doing the first step, is located between rocks directly west of the Nomads' Camp waypoint and east of the 
Bathing Spot interesting site near Rocktower Pond.
The easiest way to get there is to travel to the Nomads' Camp waypoint, then get on the path leading west and then southwest from the waypoint. From the travel point, it is left, through the campsite on the image below and past Bibrek the Archer from Horses for Courses task.
Continue along the path and notice a barely visible path left into the hill.
Wolf fight and Mutt
Follow it until it ends near a large cliff drop. Go around the drop to the left and try to descend until a cutscene starts where Henry finally reunites with Mutt.
That is not all though, a pack of six wolves is waiting. Try to keep them all in your field of view. A wolf attacks roughly every five seconds. The safest strategy is to parry and immediately counterattack. After a successful parry, press attack almost instantly so Henry performs a hit (or on a Lent run, a kick). This deals strong damage.
Now you can also sic Mutt at the enemies, which will be very helpful during the fight with six wolves.
Rewards
The quest is finished after the battle and while there is no specific reward for it, go into the stone cave to find a stash with a Gemstone Silver Ring, Spectacles, Tin cross, some meat and 4 Groschen, making it a very strong reward. There is also a Cuman Bascinet nearby.
Houndmaster tutorial
You can read the Houndmaster tutorial for Mutt here:
Mutt Quest FAQ
When can I start the Mutt quest in KCD2?
Right after the prologue. In your journal under Mutt you usually get "Find out what happened to Mutt." with a marker northwest of Bozhena's Hut.
Do I have to talk to Bozhena before the wolf den?
Not for the shortcut. You only need the first site northwest of Bozhena's Hut (bandit + corpses). Then Mutt unlocks on the map and you go west of Nomads' Camp.
Do I have to visit Bozhena, Vostatek, and Siegfried during the Mutt quest?
Only if you follow every journal marker. For the shortcut you skip that tour after the first clue. Bad Blood, Lackey, Sheep among Wolves, and those NPCs stay available later.
Where is the wolf den on the map?
Between rock formations west of Nomads' Camp and east of the Bathing Spot near Rocktower Pond.
How do I beat the six wolves at the Mutt den?
Keep them in view. Parry and counterattack right away; on a Lent run use kicks after parry. Once reunited, sic Mutt to distract and damage wolves.
What is in the Mutt den cave stash, and what does finishing the quest unlock?
In the stone cave: a Gemstone Silver Ring, Spectacles, Tin cross, some meat, 4 Groschen, and a Cuman Bascinet nearby.
Finishing the quest unlocks Mutt, the Houndmaster skill tree, and sic commands in combat. The quest itself has no extra item reward besides that stash.