Building up relationships in Persona 5 is a little different than in other RPGs. Occasionally, you'll need to build up different stats before you can hang out with someone and further your relationship. Other times, it's best to buy them a gift. Just like in real life, though, not every gift works for every person.
Persona 5 gift guide
Samurai Gamers has the ultimate gift guide for Persona 5, from what I can tell. It's just a big ol' list of everything you'll ever need to get for anything, and where you can get it.
The majority of the gifts can be bought from the underground mall in Shibuya. If you ever see something in a shop that doesn't seem useful in battle, it might be a gift and you should buy it. For example, you can buy Red Lipstick from the underground mall, which Ann Takamaki likes as a gift. If you know each character well enough, you can intuit what they might like as a gift.
Remember, maxing out friendships is useful on a number of levels. Sure, it's nice to have friends you can confide in, but it also helps you create the most powerful Personas possible. You better be in the gift-giving mood if you're playing Persona 5.
More Persona 5 news, updates, tips and tricks
For more on the latest entry in the Persona series, check out the rest of what Mic has to offer. Here's a guide to building relationships with the game's Confidant system, and a guide to when and how you can name your main character.