On this page of the game guide to Borderlands 2 you will find the walkthrough descriptions of the first two main storyline missions - My First Gun and Blindsided. The events of these quests play out on the Windshear Waste map.
1) Starting point
2) Claptrap's hideout
4) Claptrap Eye
5) Claptrap (mission completion) and a teleport to Southern Shelf
After gaining control over your character , follow the Claptrap south west  to his hideout.
After you get there , wait for the robot to open the door and head inside as well. Follow the tunnel deeper into the cave.
After you reach the middle of the cave, approach the Claptrap in front of the oven to watch a short cinematic.
Claptrap will lose its eye. Your first objective will be obtaining weapon from the locker in the southern part of the cave .
After picking up the weapon, wait for the Claptrap to open the next door in the southern part of the cave. Search the chests in the room and turn on the Fast Travel. Go through the next door in the south of the cave to reach an open area.
Follow the Claptrap while opening chests and breaking the ice which you will come across. After reach the place visible in the screenshot, you will be attacked by the first group of Monglets.
After getting through the cave, you will reach a precipice by which you will get attacked by Monglets again. After defeating all of them, jump down and help the Claptrap to get out of the snow.
Afterwards head further to the passage where you will find a few chests. Search them.
Move onwards and you will be attacked by a Knuckledragger and Monglets. Keep your distance and shoot the enemies while looking out for stones and jumps made by the Knuckler. Break ice to get more ammo and restore health. You can also retreat to the previous area to find item you didn't pick up before.
After killing the Knuckler, pick up the Claptrap's Eye . The item might be invisible at first, but you should be able to pick it up if your get close enough.
Now follow the Claptrap up and eventually the door will be unlocked. Inside you will find an item chest and will be able to finish the mission by speaking to the Claptrap .
Now approach the door to move to Southern Shelf.