On this page of the game guide to Borderlands 2 you will find a detailed description of the side mission titled Get to Know Jack. You can begin completing this quest during your first visit to the Arid Nexus Badlands location. This happens right after you complete the storyline mission named Data Mining.
Arid Nexus Badlands
1) Bounty Board
2) ECHO Journal 1
3) ECHO Journal 2
Arid Nexus Boneyard
4) ECHO Journal 5
5) ECHO Journal 3
6) ECHO Journal 4
From the Bounty Board  you will receive a mission of collecting five Jack's ECHO Journals. The first one is in the building marked as , on a shelf. Inside there's also a weapons chest.
The second one is on the roof of the building  from the above screenshot. To get there, jump from the balustrade onto the roof of the smaller building. From there head onto the main building's roof to pick up the recording.
Now go to the passage in the southern part of the map to reach Arid Nexus Boneyard. For the next recording, Use the lever from the above screenshot . That way you will activate a fan which will lure the Rakki from their nest. Shoot the one with the Recorder.
Journal 3 can be found inside the container shown in the screenshot .
Journal 4  is inside a garage from which a couple Robots and Hyperion Soldiers will come out. After collecting all recordings, return to the Board  and end the mission.