The Magician Arcana
The Magician Social Link is one of the first ones you'll gain access to in Persona 3. It is tied to your classmate Kenji Tomochika who you can find in your classroom on Tuesdays, Thursdays and Fridays. There's no special requirements to begin this Social Link.
It's important to note too that you'll have to raise The Magician Social Link to roughly rank 3 or 4 in order to unlock "The Moon" Social Link. Kenji will mention The Gourmet King at some point during your friendship and that's who The Moon SL is tied to.
While raising a Social Link you'll be given story cutscenes where you'll have to answer questions. The answers to each of these questions is different depending on the person and the situation. What you usually need to try and do is pick an answer that reflects their personality. Here's a cheat sheet for each Social Link rank of the Magician Arcana and what to say.
Rank 1: Automatically earned
Rank 2: That's a secret - I like older women
Rank 3: What, life? - Go for it
Rank 4: Anything - Good luck
Rank 5: I agree
Rank 6: Anything - I have 30 year goals
Rank 7: ((Ask What's wrong)) - Bride to be Magazine - That's Great - Congrats
Rank 8: Are you in trouble? - You should talk to her
Rank 9: ((Confront Emiri))
Rank 10: Automatically earned
When you complete this Social Link you'll be able to fuse Surt through normal or triangular fusion. Surt is pretty powerful and can learn the ultimate ability Ragnarok later in the game.