The first non-DLC* tomb you will encounter is the tomb of the unworthy. You need the climbing axe to complete it, but as long as you're following the story you should have it by that stage.
The tomb is at the top of the mountain village area behind a waterfall. There is a symbol painted on the cliff face near the entrance, so it's relatively easy to find.
Once inside, you'll see a platform and a cage suspended from rope. There are three mummified bodies hanging upside down inside the platform.
Jump on the suspended platform and quickly jump across to the small alcove with the lamp. Light your torch and then jump back across to the platform with the bodies. Set all three alight.
Make your way back up to the cage and press Y to push it off the edge. It will fall and drag the now-empty platform into the air.
Jump on the platform, and then jump again onto the wall to the left. Press X to use the climbing axe and then climb to the top to enjoy your loot.
* The DLC tomb (Tomb of the Lost Adventurer) in Coastal Forest is the first you'll encounter if you have the DLC. You'll find it after meeting up with Samantha. Follow the right edge of the map from the zone's start area until you encounter wolves while going to meet Whitman. It has a large painting of a goddess on the cliff wall above it.