Terminal 1 (Requiem) - Towards the end of the mission "Requiem" (after taking down the two hunters and getting access to the tower) you'll see a large ramp. The terminal is located underneath the ramp.
Terminal 2 (Forerunner) - Near the beginning of the mission "Forerunner", when the Chief asks Cortana "What's that distortion?" you'll see a large structure embedded within the the rocky environment. You'll find the terminal at the base of the structure.
Terminal 3 (Infinity) - During the level "Infinity", right after you watch the cutscene in which the Chief meets up with some fellow soldiers, the terminal will be directly behind you.
Terminal 4 (Reclaimer) - Once you reacquire Cortana in the "Reclaimer" level, exit the room, but before going on the elevator, travel down the hall on the right. The terminal is down that hall.
Terminal 5 (Shutdown) - When you reach the production tower in "Shutdown", don't follow Cortana's waypoint to the right. Head forward to a structure at the back of the room instead, and you'll find the terminal on the far side.
Terminal 6 (Composer) - After the Chief meets Tilson in the level "Composer", head outside and look for the Atrium. Just below the "Atrium" label on the right side of the building lies the terminal.
Terminal 7 (Midnight) - Once Chief is grounded on the level "Midnight" check behind the central pillar in the third room you enter. The terminal will be behind that pillar.