Right after you defeat the first two armored Hunters you need to enter the building and look under the main ramp (the one that goes to the elevator shaft). The ramp is transparent.
2nd Terminal - Forerunner
During the mission Master Chief's HUD will flicker and Cortana will say "What's that distortion?". When this happens, you will find the 2nd terminal dead ahead at the bottom of the Forerunner structure with three columns.
3rd Terminal - Infinity
After you meet with fellow USMC soldiers and there is a cut-scene, turn around and the terminal is right behind you. Easy!
4th Terminal - Reclaimer
Right near the end of this mission, after you get Cortana back, you will be asked to escape using an escalator (there is a cut-scene too). After this, backtrack through the level a little and there will be a lightbridge taking you right. Get off the bridge and turn right and ask you go down that hall you'll find the 4th terminal.
5th Terminal - Shutdown
When you get to the Production Tower (the third one), Cortana will tell you to find the control room. Take the elevator up and then cross the bridge. Here you will need to kill two hunters. Then turn around and face the lightbridge you just came from. Go to the right of it to reach a new platform and the 5th terminal is at the back of it.
6th Terminal - Composer
Once you kill the two hunters there will be a long cutscene. After it finishes, look directly ahead to find a building with the name "ATRIUM". Below this building in a cave is the 6th terminal.
7th Terminal - Midnight
Once the flying sequence is over and you fight through several Promethean area, you will come to a third room. Look behind the center pillar/structure for the 7th terminal (some say this is in the fourth room, so if you can't find it at first, go to the next room).
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