There are a total of 7 terminals available in Halo 4, as follows:
] - Location 1: Requiem
At the end of the level, after defeating 2 hunters, you will come to a long hall. At the end of the hall you will view this terminal in plain sight under a clear ramp that leads to the end.
] - Location 2: Forerunner
During the mission, near the beginning, you will defeat a small group of crawlers and a promethean knight outside in an open area, and your HUD will begin to become distorted. Masterchief and Cortana will begin speaking about the signal distortion, and masterchief will say "What's with this distortion?". Once this happens, the terminal should be on ground level, under the next objective.
] - Location 3: Infinity
After meeting up with your teammates, there will be a short cutscene and you will spawn inside a ship. Just turn around and the terminal will be directly behind you.
] - Location 4: Reclaimer
Midway through the level, after the first main cutscene, you will end up indoors. You will have to pick up Cortana and make your way through a hallway. Instead of boarding the elevator (primary on-screen objective) take a right and the terminal should be there.
] - Location 5: Shutdown
When progressing through this mission, you will come to a section with a bunch of light bridges. At one point you will reach the end of the path and two hunters will appear. The terminal is directly before this checkpoint, but you can easily backtrack. When going from the entrance to the location of the hunters, take the last possible left and the terminal will be located behind the structure on this platform.
] - Location 6: Composer
Once you reach the outdoor part of this level, run across the terrain to the building that says "Atrium" on the side. At the base of that sign is the Terminal. The "Atrium" sign does repeat itself on the side of the building, but this is one the closest and in the most clear sight from where you begin this section.
] - Location 7: Midnight
Once you get to the part of the level where you are in foot, progress through the story by clearing the rooms of enemies and moving forward. Once you enter the 3rd or 4th room, you should see the terminal located behind two pillars. Walk around to the back side to access it.