Dragon Age: The Veilguard has brought back the age old tradition of gifting things to your companions to make them like you more. Unlike in Dragon Age: Origins, this isn't a guessing game where you need to find out by trial and error who likes silver necklaces and who get revved up by ancient scrolls. Things are a lot more obvious and you basically can't screw this up, so long as you can locate them all.
In Veilguard you cannot give gifts to the wrong person by accident. Each gift is clearly labelled with who it's for and when you acquire it you'll get a small side quest telling you to go give it to the relevant companion. You also can't accidentally sell a gift instead of giving it to a party member, so you're protected from that mistake as well. Really the only task here is figuring out where to get each gift.
Veilguard gift locations
In Veilguard there appears to be just one gift per companion that you can give. Each one is sold by a merchant for the faction that companion belongs to. You can find gifts in the "Valuables and Collectibles" tab with the relevant companion's portrait next to it. I wasn't able to find any additional gifts by upgrading to the max level of the faction merchant or completing my companions' quests, so I'm pretty sure it's just one gift per person.