Mountain Caves. Doesn't that sound scary?
This is your first checkpoint too, whenever you save a game, you restart from the last checkpoint. The game also autosaves, so next time you want to play, just Resume the game.
Jump on the rocks to the left, use the grappling gun to swing across, then jump up and press the button to open the door.
After a short cinematic where you can admire Lara's jumping and shooting, it's tine to get back to your quest.
After you go a bit forward, you notice the well-known Tomb Raider famous dart traps. These are quite easy to avoid, just watch their sequence and roll forward when it's clear (use SHIFT + forward).
Just do some running jumps next and you're past the bridge.
You can then go to the right and discover your first artifact. At the last ridge, go forward until Lara starts to slide then press JUMP+Forward.
If you did go and pick up the artifact, you can next jump and grab to the ledge ahead, if you didn't you'll get to the same place by choosing the left path.
Now you'll be able to practice your shooting for the first time, 2 bats are coming to greet you. Just point and click, Lara will aim at the enemy, you can also hold the RIGHT button for extra moves, but you'll have plenty of time to practice that later.
You come to a crossroad next, you can go to the right for a big health pack (you don't find these too easy so why not?). All you need to do is to jump to the nearby rock then do a running jump to the ledge ahead.
Then go to the right side. Two more bats will come to bug you.
You finally reached a bigger cavern.
You can jump then grapple to the ridge ahead, then follow the ledges to the left until you get to an artifact, or you can just slide down and continue the level.
Pull the lever to open the door, then continue forward.
Since you are here, you can go for Artifact #2.
You get to a bridge that even a 10 years old kid can tell you it will collapse and with the howling you hear it's pretty clear you'll have to fight. Two wolves will jump you as you fall into the pit. They can do quite a bit of damage, just be sure you jump a lot and don't stop shooting.
When you're doing playing with the wolves, jump to the broken bridge and climb up.
Next you can go for the small health pack, when you're done, continue along the next bridge (which with a bit of luck didn't collapse).
Next you'll need to swing across a crack using a rope. You can also swing to the small cave to the left for a large health pack. If you fall down, make sure you climb a rock or jump a lot, there's a bear waiting for you there.
After you kill the bear, you can go to a hidden room which leads to the previous room where you were ambushed. I'm still not sure what the use for that is though.
After you swing across the gap, you can find a small medikit behind the second pillar on the left.
Continue and you'll need to do some jumping, use a bar ahead to swing across the gap and you'll get to the "deadly dart trap room" part.
Don't worry, you just need to watch the darts and roll when it's safe. If you don't get the timing right, try to move to the left to have a bit more time to react).
When you get past those traps, you'll reach the massive door which seems to have two locking mechanisms.
Use the ledges on the left side to climb up. A wolf will rush in, so have your weapons ready.
Jump the the ledges ahead and you're done with the first lock. Since it only lasts a limited amount of time, you should hurry up to get to the other one.
Jump across to the other side using the bars, where 2 more wolves will rush in. Kill them quickly and continue to the locking mechanism.
Use the ridges to the right, then do a back jump to the bar and finally swing across to the locking thing.
With both locks open, go down, sit on the opening pad and tada, the door is open.
And with that last step, you just finished the first level.
Before you leave though, you can go get the Killer Whale Bottle relic.