The Aspect of Influence is the first aspect that is available during the Season of the Chosen. To start this quest, you will need to visit the Exo Stranger on Europa. Speak with her and she will give you the quest.
After that, it is off to the Asterion Abyss, then down in the Well of Infinitude. There will be plenty of enemies to kill along the way, but nothing that should cause you any real trouble. You will need to have the Salvation’s Grip Exotic equipped, as there will be some Stasis Shards that you need to destroy. This portion is fairly straight forward as all the Shards will appear on a straight route to the end of the Well of Infinitude and are extremely hard to miss.
Shoot them all with the Salvations Grip and then prepare for some good old Vex shooting. Waves of enemies will spawn in, eventually culminating with a yellowbar Harpy Exemplar that is quite a tough customer. It is a good idea to save your ultimate for this guy, and bring something that does a lot of single target damage.
After that, you will need to complete the Heroic Exo Challenge. This week is Safeguard, which is a little tough at Heroic level. You need to repeatedly clear all enemies before they can invade the upper levels. There will be plenty of Overload champions, so make sure you bring your Artifact mod that will help you deal with those.
If this is too tough, as it should be a 1270 Power activity, you can just wait until later in the season to complete it and get the Aspect then, or just team up with some buddies for an easier time with this challenge.
Once that is complete, you can head to the Ziggarut on Europa and confirm your new Aspect.