On this page of the game guide to Borderlands 2 you will find a detailed description of the side mission titled Mine, All Mine. You can start this quest in the Sanctuary location after completing the main mission named A Train to Catch.
Talk to Lilith  in Roland's hideout and accept the mission. Use Fast Travel to move to Tundra Express. There head to the northern part of the map, to the mine . As you enter the area, you will be attacked by Miner Rats and Bandits. After you kill 10 Miner Rat, you will have to take care of Prospector Zeke. To reach him, you need to get to the upper part of the mine by using the line from the above screenshot. Be careful not to get crushed.
As you reach the upper level, you will have to fight with Zeke. You can receive bonus experience by killing him with a Slag Elemental Effect weapon. After clearing the area, pick up the ECHO Recorder "The Deal". Head back to Tina  and talk with her to end the mission.