This page of the Aliens Fireteam Elite guide offers a walkthrough for Search, the mission of the fourth campaign (The Only Way To Be Sure).
First, you will have to break through the nests of Aliens. Therefore, be prepared that every now and then you will be attacked by Xenos.
As you walk from marker to marker, be careful in the corridors next to the main path. More Xenos will emerge from it. You may also encounter enemies who will try to ambush you.
In the new room, your task will be to collect several dog tags from the bodies of another team. Every time you pick up one of the dog tags, you'll be attacked by the Xenos.
A chest with supplies, ammo, and a first-aid kit is to the right of the soldier with the dog tag. Before you pick up the dog tag, take everything you can. Next, pick up the dog tag and start fighting the Xenos.
When going through a narrow corridor, you will encounter more Xenos. When reaching the surface, there will be a Xeno hiding on the left side - it will grab you if you do not react quickly enough. More Xenos will come.
When you're at the bottom, you'll discover Xeno nests. There will also be eggs, so it is worth shooting them from afar first so that facehuggers won't hatch from them.
Then go to the next markers appearing on the radar - you reach the place where you will need to gain access to the console. A box with supplies is on the left side of the console - before you interact with the console, get everything you need.
You will face more Xenos. The majority of them will be the regular Xenos. However, over time, you will also face much stronger versions, such as the Praetorian.
Go through the door of Deck 24 - you will find another dead Marine soldier. Take the dog tag from his body, and then proceed to the room with supplies.
When you have replenished your supplies, pick up the last dog tag to trigger a wave of Xenos. Be on the move at all times, because now you will be attacked by a very large group of Xenos.
In addition to the standard enemies, there will also be warriors and Praetorians. Do not stand still when you spot them, move around and shoot at their weak points. When you defeat all the Xenos, approach the new marker to complete the mission.