On this page of the game guide to Borderlands 2 you will find a detailed description of the side mission titled 3:10 to Kaboom. You can begin this quest in the Lynchwood location during the completion of the side mission named The Bane.
1) Bounty Board
4) Explosive train car
5) Rail tracks
Use the Bounty Board  to receive this mission and head to the refinery . In order to get there, you will have to use the elevator . A timer will start counting and you will have five minutes to complete all the tasks. Start from Using the lever from the above screenshot.
Afterwards press the button behind your back. Eventually a car with an explosive charge from the above screenshot will arrive . Take it.
With the explosive, head to the rail track marked as . Place the explosive in the designated place and run to the detonator . Wait for the car with the explosive to be below the train (square) and detonate it. Now you can return to the Board  and end the mission.