Some people have trouble with this so I will be glad to help.

Terminals 1-3 are all found on the level, “The Ark”. The first terminal is found the first time you walk inside (in a small hallway). The second is located right next to the control panel that lets the Scorpion tanks across the bridge. The third is located under a set of stairs after the room with the sleeping Grunts.

Terminal 1: The first time you go inside, you will see a door almost immediately on the left. Simply enter this area of the level to find the first of the seven terminals.

Terminal 2: When you go inside the structure to let the tanks across the bridge of light, there will be a Terminal almost directly behind the controls for the bridge. It’s an easy find! You must activate the bridge and go access it quickly or it closes up.

Terminal 3: You’ll miss this terminal if you are not careful. After defeating the scarab, you will head into a large structure. There will be a room with several sleeping grunts. Nearly directly following this room is another room in which you can take two different directions. There is a door, and a staircase (both eventually lead to the next room). Underneath the staircase is an additional door that leads to the 3rd terminal.

Terminals 4, 5, and 6 can all be found on the level, “The Covenant” on Halo 3. Each of the three shield generator towers has a terminal in it. Tower 1 and 3 both have the terminal near the elevator leading up to the shield controls. Tower 2 has the terminal just near the top of the ramp (on the opposite side of the Thunderstorm Skull Location).

Terminal 4: When you access the first Elevator leading to the tower controls, jump from the elevator platform to the platform on the opposite side from where you accessed the elevator from. The terminal is dead ahead.

Terminal 5: After getting a Hornet vehicle, fly towards tower 2 (the one that the Arbiter has already disabled). A voice will remind you that Tower 2 is already clear, just to confirm you are at the right place. The Terminal is just inside of the structure.

Terminal 6: Terminal 6 is identical to Terminal 4, only in the 3rd tower. Just jump to the platform, and there it is!

Terminal 7: Terminal 7 is found at the beginning of the final level in Halo 3. To find it, simply head forward from the start of the level, until you encounter the area with a few structural beams going from one wall into another. At this point, turn right, and look for beam separate from the rest (as highlighted below):

Secret 8th Terminal: The Eighth Terminal can be found on the level, “Cortana”, and is located on the basement floor of the room with the “Tilt Skull” in it. At the very bottom of this room, there is a Gravity Hammer leaning against a stand. This stand is a Terminal (although it does not look like the other terminals in the game, it simply looks like a pedestal of light). Upon accessing it, Cortana will take over your HUD with a brief message, which is a reference to the Novel “The Fall of Reach”, according to Avateur over at ABO. However it does not count towards the achievement and getting it won't help you get the achievement.

All info is courtesy of www.halo3palnet.com