Sentinels are small companions that will follow you around, and assist you in different ways depending on your Sentinel and mod choice. In order to build a Sentinel, you'll have to purchase the Blueprint on the Market (Market > Equipment > Sentinel Blueprints) or through Clan Research and build the Sentinel in the Foundry afterwards. You can also directly buy a pre-built Sentinel with Platinum.

While each Sentinel has it's own specific roles and weapons, I would advice using the Carrier Sentinel, since it has a strong shotgun as its weapon and most importantly a Vacuum mod that picks up all nearby loot, allowing you to hardly ever miss any resources, which you'll need for building nearly everything in this game.

Once you've built a Sentinel, go to your Arsenal and equip your Sentinel. Your Sentinel consists of the Sentinel itself and its weapon. You'll have to reach level 30 with the Sentinel itself to obtain this trophy. Your Sentinel will gain experience for killing enemies and activating abilities, which are applied by adding mods. In order to quickly level your Sentinel, it's advised to upgrade your Sentinel's weapon with general weapon mods and your Sentinel with Sentinel specific mods whenever possible.

For your Sentinel's weapon, go with any damage mods. Don't use mods such as increased ammo, these are wasted mod points on a Sentinel. Depending on which Sentinel you've obtained, the weapon type can be the same as your Primary weapons (Rifle, Shotgun or Pistol), which will also use those same exact mods. Therefore, you won't be able to use your weapon and a Sentinel weapon at the same time if they have the exact same mod equipped.

There are only a few Sentinel specific mods that will grant the Sentinel Affinity (experience) wben being used:

Ghost (Shade Sentinel)
Guardian (All Sentinels)
Regen (All Sentinels)
Sanctuary (All Sentinels)

Other than that, there's nothing more to it. Simply keep playing the game with your Sentinel equipped and it will level up. If you don't have any mods that might help out, don't worry, you don't need to apply any mods for it to level up.

The total Affinity required to level your Sentinel to Rank 30 is 900,000. You can check the total amount at your Profile > Sentinels.