Make sure to loot all the containers around you. There is lots of ammo in the crates, which you will definitely need. There is also a lot of money on a square table in the center of the room, where some robots appear to have been playing cards. Claptrap exits through a trapdoor and opens some other door, through which you can follow him into the other room. Again, search the area well for supplies. Ammunition is EXTREMELY important in this game. If you played the first Borderlands, you know this. Wait for Claptrap to open another door, then follow him outside.

Claptrap tells you that you he is sure you will find the eye Knuckle Dragger stole in Frostbite Crevasse. The mysterious guardian angel contacts you again, she suggests you stick close to the robot. He will help you get off this glacier, and into the city of Sanctuary. That is the only place you will be safe.  Keep following Claptrap. Soon you will have your first combat, against small Bullymongs called "Monglets". These shouldn't pose much of a threat, shoot them with your gun. This is a good chance to practice fighting and shooting. If you have training messages enabled, you should see prompts telling you what buttons to push to perform different types of attacks.

When fighting the Monglets (and future enemies you encounter), be sure to aim and do NOT fire aimlessly in the air. You don't want to waste bullets. I cannot emphasize enough how important ammunition is, and if you waste your bullets you will regret it later. If you are using the starter pistol, Basic Repeater, zoom in on the Monglets to take advantage of the burst fire.

After killing all those Monglets, first make sure to pick up any items they dropped. Then, keep following Claptrap, who warns you that if you don't get his eye back you will never get to Sanctuary. Smash the flashing rocks around the area to reveal more ammo and money. Claptrap can be annoying at times, but the mysterious woman tells you that you need his help to get to Sanctuary, where you will be safe. Sanctuary is the last standing bastion of resistance against Handsome Jack.

Soon you reach Frostbite Crevasse. Fight some more Monglets, and go deeper into the Crevasse. There are also some Brat Bullymongs here. Claptrap becomes stuck in a hole, interact with him to dig him out. Follow Claptrap up the platform. Soon he detects that his eye has switched on, so whoever has it must be close.

NOTE: The next fight will be pretty hard if you are new to the game. If you haven't already, open your inventory and check what other guns you have. If you are a Premiere Club member, you should have some additional, more powerful guns in your inventory.

Knuckle Dragger Strategy
Knuckle Dragger can be pretty tough to beat. Open all containers in the area and remember where the "Health Now" packs are and where additional ammo is. If you run out of ammo or health during battle, run and resupply. Knuckle Dragger has some minions, get rid of them before focusing back on Knuckle Dragger, though if you are about to die, keep one minion alive so that you can kill it during the "Fight For Your Life" phase. (See below)

Be on the move constantly, and evade Knuckle Dragger's leap attacks and object hurls. If those hit you, you will lose a substantial amount of health.

If you run out of ammo, switch to another weapon (if you have one), otherwise you will have to use Melee.

Be sure to reload when your magazine is low and you have a chance. You don't want to be forced to reload at a critical moment, since reloading costs valuable time.

If you lose all your health, you don't die immediately. First you enter a "Fight For Your Life" stage, where you can prevent your death ("Second Wind") if you can get a kill before the timer runs out. Whenever you are in that stage, you need to focus on the WEAKEST enemy, one that you can kill the fastest. If Knuckle Dragger's minions are still alive, target one of them.

If you do die, you will respawn nearby in a New-U machine. Check the containers near the machine for more supplies, and run back into battle. When the whole party dies (or if soloing, when you die), Knuckle Dragger will go back to full health and you will have to start over. So you naturally want to avoid dieing, if possible.

Claptrap's Eye, which was stolen by Knuckle Dragger, in Borderlands 2

After defeating Claptrap
Retrieve Claptrap's Eye, use waypoint to locate it. Pick up money and other items that are laying around.

You have to find someone who can fix Claptrap. Claptrap suggests his friend, Sir Hammerlock, in Liar's Berg. Your objective is now to find Sir Hammerlock. Liar's Berg is on the other side of the Hyperion Barge. Claptrap tries to open it, but fails. Luckily, the mysterious woman unlocks the door for you. She explains that the perks of being an Artificial Intelligence is that she is networked to almost everything on this planet. She also says that is is a long way to Sanctuary and suggests you take whatever you need for the journey ahead.  Look around to find new gear, then loot the gear. There is lot of supplies in this room.

When you are done, turn in the mission to Claptrap. This completes the mission, Blindsided, and begins the third story mission, Cleaning up the Berg.