On this page of the guide to Aliens: Fireteam Elite you'll learn how to complete the first mission called Ingress from the first campaign called Priority One.
Once you enter the map, the first thing you need to do is to go to the newly appearing points marked with a black-and-white rhombus. Going further, you will come across a console that you need to activate.
Then, moving on, you need to pick up an object located near the two boxes. When you do, you will be attacked by Xenomorphs.. Keep an eye on your radar in the lower right corner so you don't get caught off guard by new enemies.
The enemies will approach you from the opposite side at first, and once you defeat them, they will start attacking from the right. They are the most common Xenomorphs, so they shouldn't hurt you. When you defeat them, go to the next point.
In the meantime, as you move from room to room, you will come across an ammo chest. This is a good time to replenish your supplies, as things are about to get tough.
For a while, you will be forced to defend yourself against overwhelming enemy forces. In addition, a new, green kind of Xenomorph will appear, and it will shoot acid at you from a distance. Try hiding behind the barricade.
When you defeat the enemies, go to a new point, then prepare for another fight. Replenish supplies, open the item chests, heal yourself if your health is low, and pick up a new first aid kit. Then, before activating the console, lay out the mines, turrets and other supporting items that you got from the crates.
Now you will have to defend the location you're currently in. Every now and a new wave of enemies will come. You must survive as long as possible, defeating all the waves. Watch the radar - it will make it easier for you to detect and quickly eliminate new enemies.
Next, you will have to break through more enemies, open the door and then download the data from the server.
The final objective of your mission will be to hold your position for a few more minutes. Just like before, regenerate your health, refill your supplies and prepare for battle. There will be a lot of Xenomorphs, so there is no point saving the auxiliary items, especially since this is the last objective of the mission, and if you die, you will have to replay the mission from the beginning.
Aside from the standard Xenomorphs, there will also be a Xenomorph Warrior, which is a very durable type of opponent. Shoot him in the head and use all special skills, because he will be the biggest threat. When he attacks, make a dodge at the right moment to avoid taking heavy damage. It's best to have skills that can stun him for a while.
Additionally, listen to the Herrera's messages - he will tell you where the enemy will appear and what kinds of Xenomorphs you can expect in a moment.