Throughout your time in Baldur's Gate 3, you'll have many chances to recruit various pets to your cause, some of which can assist in battle and/or questing while others will just serve as company and/or item fetchers for you.
Us is a mind flayer minion you can add to your party at the beginning of the game, and it'll be a big help before you acquire more party members.
From the very start of the game, use the Jump action to reach the upper left platform. Continue north into the next room and interact with the Neural Apparatus to ascend to the upper left platform.
Talk to Myrnath to the left of the platform. Passing the Arcana check will reveal you're talking to an intellect devourer, a mind flayer minion. An Investigation success will cause you to notice swelling; a Dexterity success will make it docile. In any case, freeing it from the body will cause it to sprout legs, after which it will ask you to go to helm with it. Us will now join you if you're interested.
Travel slightly west of Silvanus Grove (X:153 Y:374) and take the Cragged Rock to the high ground. If you pass the Perception check, you'll notice a spider egg nest nestled between some rocks in the corner. Pass the checks and they should join you; fail and drop then attack the egg you acquire to spawn a swarm that will follow you around.
This one will require a truly monstrous action: killing the cub's mother. To find both, head to Owlbear nest and take down the beast, then let the cub live, which will eat its mother for sustenance.
Head to Goblin Camp on the west side of the map (X:-106 Y:421) and look to your left. Speak to the female goblin about "chicken-chasing" and agree to play. Upon catching the "chicken" (owlbear), convince it to turn on its masters and wipe them out right there. Alternately, tell the woman once the game is over that you're leaving with the owlbear. She'll require convincing if you don't want to fight but either way, you get your owlbear (assuming you survive).
The animal will now appear in your camp if you rest. When you interact with it, you'll be given multiple opportunities to care for it.
Find Scratch in the forest slightly northeast of Blighted Village (X:81 Y:471), where you'll find him mourning his dead owner. Passing any of the checks then letting him smell you will be enough to recruit him to your camp. There you can play fetch with him, pet him, and receive items he brings you.