After Priority: Thessia, head to Horizon in the Shadow Sea cluster to investigate Sanctuary. There are no enemies visible immediately after you land, so head up the stairs, a Cerberus shuttle crashes ahead of you. Two Phantoms and a Nemesis Sniper emerge from the shuttle.
Try to kill the Phantoms at a distance while staying in cover to avoid getting shot by the Nemesis' sniper rifle. Once the Phantoms are taken care of, get out your sniper rifle or pistol with scope to take care of the Nemesis. Once you open the door, there's a Med Kit immediately to the right of the entrance. Look up to see another Cerberus shuttle, then explore this floor of the building before heading downstairs. There are various consoles and PDAs that tell the story of what went on here, and some ammo on one of the tables.
When you're done, head down the stairs. There are some PDAs that provide back story on the left, and some dead Cerberus troops and Reaper forces in the room on the right. Keep your guard up, because there are a few live Cerberus Assault Troopers in the room past the dead troops. The exit is an open doorway on the left side of the room under the massive Sanctuary sign. Activate the console to hear what you're up against and get a glimpse of Miranda Lawson (so long as she didn't die in a Mass Effect 2 save you imported).
Head outside. Ignore the dead Cerberus soldier floating in the water and activate the water pump. The water lowers, allowing you to climb down. At the bottom of the ladder, head right until you come to a door. Proceed back inside. There's nothing in this first room. As you approach the door, one of your squad mates muses that this is going to get ugly. Proceed to the next room, which is a command center of sorts. Activate the console in the middle of the room to restore power. Don't worry, the things you see in the cut scene can't hurt you. The tower is now marked on your HUD. Proceed through the now-unlocked door opposite the one you came in.
In the next room, there is a PDA on the table on the left that you can safely ignore. There is a console in the far right corner of the room that provides more back story and a glimpse of The Illusive Man and Kai Leng. The exit to this room is down a short set of stairs. There are a bunch of Husks behind the door, so get prepared before you head down the stairs. In the room where the Husks used to be, there are two logs which can be activated for story at the bottom of the stairs. The open doorway and the regular door near the consoles both lead to the same hallway. There is a bunch of Reapers out there: a Ravager, a Banshee, and a few Marauders shooting at you from a catwalk above. Kill them in that order, ducking back into the room with the consoles for cover if you need to. The exit is down the hallway to the left. Pick up the Med Kit and ignore the Banshee staring menacingly at you through the window. You can activate the two logs for story but they won't let the Banshee out. Exit through the door.
The next room has a set of stairs on the left. Go forward first and activate the console for story. Continue past the console to find a PDA and other goodies. Head back toward the door and go cautiously up the stairs. Through the open doors on the left is another room full of Reaper forces. Ignore the Husks in the pods (they don't come to life) and focus on the Cannibals and Marauders. If you take cover between the two doors, you should be able to destroy the Barrier Engines through either doorway without taking fire. That will make your fight a little easier.
Once the room is clear, head to tables and consoles in the middle of the room. There are two logs you can activate for story near the middle of the room. Proceed to the far end of the room. There is a PDA that provides more back story. Activate the Console at the far end of the hall on the left side. Climb up the ladder and get ready to fight. There's a Marauder fairly close to you, so take him out first. There are Ravagers and Cannibals farther down the hall. Get up on the raised ledge and peer down the support columns to take out two Barrier Engines with the Sniper Rifle.
Take them out from a distance if you can. There are also some more enemies lurking in the dark on the right of the lit hallway. Once the enemies are clear, make your way through the open doorway at the end of the hall. A Med Kit can be picked up just on the other side of the door. At the far end of this relatively dark room, there is a log you can activate in the left corner next to a display window. Despite the dialogue, no Husks are released. Exit through the open doorway on the right side of the room. Jump across to the next platform, then shoot the panel on the floor to expose the controls. Ride the lift to the other side of the room, then jump across again to the door. Ignore the Husks running amok at ground level because they won't hurt you, but be prepared for a fight when you open the door.
Once you open the door, you will see some burning rubble. Look to the right to see a Brute. There are actually three Brutes in this room, plus a Banshee for good measure. One of the Brutes is actually pretty close to you, just beyond the burning rubble. Keep your distance and wear them down. If you're facing down the hall (as you were when you were instructed by the game to look at the Brute), there is ammo in the dark area on the right side of the room, and a med kit in the well-list area on the left side of the room. After the area is clear, you'll find a console and a Husk pod that can be activated to get some cool loot. Open the door at the far end of the room to enter the elevator, which takes you up to the tower.