You'll get a couple messages while first entering the Lair about ambushes and a deadfall trap.  Though important you have to keep going, so just ignore them for now.

 

Through this cave are a lot of Ursagi, Bears and Goblins, so be prepared to fight them at any time.  Note that Ursagi in general sometimes drop Ursagi Skin Armor when killed, and the Ursagi in this cave sometimes drop wands when killed.

 

Follow the passage until you get a message about an ambush being sprung, then kill the Ursagi who've appeared behind you.  You should be right near the entrance to an open area with a pool of water by this point, so stay in combat mode and enter the area to clear it of the Ursagi.  Be sure to look to the west, up a long drop to see the Ursagi up there.  Kill them using distance attacks or leave the room to the north and they'll be coming along this passage.

 

Follow this passage until you see a branch to the west.  Take the west branch and go along there, exploring the first two southern side areas for Ursagi.  The third passage to the south leads to the home of an Icy Drake.  Kill the Drake then check the ground for it's trove.  Among the various items is a book, which teaches Call Beast Lv.3.

 

Go back out into the passage and continue following it west and then north, being sure to check all side passages for Ursagi, Bears and Goblins.

 

When the passage curves back towards the east follow it that way until it splits, going north and south.  For now go south to find the Goblins area and the Bears area.

 

Now go back to the north/south passage that led out of the first open area you entered.  Go north along the passage until it branches to the east.  This leads to a small area containing some bodies.  Check each of the bodies for items, since there's a few useful things in there.  Watch out for the Clumsy Ring though, you don't want to equip it by mistake...or on purpose, for that matter.

 

Continue north along the main passage again until it breaks into three tunnels.  Explore the western one first, to prevent an ambush from behind, and then check out the northern one, which leads to an area overlooking the room the western passage led into.

 

The eastern passage leads to a rather odd experience.  Kill the Ursagi and Goblins, then approach the altar.  You can perform the Ritual of Sanctification here, but you don't get any experience, and it doesn't sanctify the altar.  Instead you'll get a message about the difference of this magical energy.  It's up to you whether you want to do this or not.

 

Now head back along the western passage, all the way to the end, battling any remaining creatures you come across.  This leads to the back entrance of the Urasagi Lair, so go out the back way, then go around to the front and enter there to pick up your horses if you had any.