Full disclosure: relationships are one of the hardest things to write as a writer. I'm not going to talk about romance in this chapter - I'm going to detour onto that topic in the next chapter, because that's a whole other can of worms. This chapter is going to be a basic guide for how one goes about writing relationships just in general. Keep in mind that this is also just some bare-bones things to think about. It's not supposed to teach you everything you need to know, but just some things to consider in your books.
Relationships between characters should be in the context of the plot. Unless both characters are at least somewhat engaged in the main story, you don't need to devote a lot of page space to them. For example, we know that presumably Catra had birth parents in She-Ra and the Princesses of Power, but they don't play a role in the story, and may even be dead. They're not mentioned because they're not important to her as a character.
But let's say this isn't your case. Let's say you have characters with lots of relationships to others in the story. There are several things you can do to make sure the reader roots for the relationship (or doesn't, if that's what you're going for).
1. Know the nature of the relationship.
When you're plotting out your characters (and I think every writer should, at least past the first draft), keep track of relationships to characters - the other point-of-view characters, side characters, and even characters not in the story. Some relationships, especially if one side is deceased, still play a role in the character's journey and psyche.
Write a few short sentences the nature of this relationship. Or, as I mentioned in Part 1 of the backstory chapters, have the characters monologue about their major relationships. Listen to what they say and where you feel they're naturally going with their response. Don't force them to say their relationship with their mother was great if it was crummy. Let them be honest, and let that influence how you write their relationships in the story.
2. Show it onscreen.
If you're writing a relationship that takes place in the present day, you need to make the reader really buy the relationship. Study your most favored relationship - what do you do with that person? How does that person make you feel? What sorts of things do you discuss (or not discuss)? How much time do you have to spend with this person, and how much time do you make for them? Knowing this stuff is essential to making sure that your relationships are believable.
3. Create conflict.
No relationship is perfect, and everyone messes up sometimes. This is where understanding where your characters are similar and different is incredibly important. If one character is emotionally intelligent and the other isn't, that's going to cause a lot of friction. And if their values and desires start to come into conflict...mm, tasty. (One of the best examples I can think of is between Elend and Tindwyl in The Well of Ascension, by Brandon Sanderson. That moment when the idealistic king crosses paths with a terse, authoritative Terriswoman to save Luthadel creates one of the most interesting student-mentor relationships I've ever seen.)
One exercise you can do to establish possible conflicts is to write down all the ways your characters are both similar and different (think: Venn diagram). Then choose the most interesting difference and experiment with that. For example, one of the main differences between Catra and Adora in She-Ra is that Adora is lawful and will always put the greater good above herself, whereas Catra prizes her personal ties to Adora and Shadow Weaver above everything, even if it makes her do bad things to get them to love her or stay with her. This causes the main conflict of the show when she decides to leave the Horde, and Catra, in the process.
Make sure that conflict between your characters is believable, though. A friend of mine once read a book in a critique circle where every other chapter, the boy and girl in a relationship would randomly fight for no reason, just to create conflict in the story. It led to the boy (usually the sweet and considerate sort) acting like a jerk to his girlfriend with no cause or reason. Characters' actions must always have a motivation that makes sense with their previously established wants and circumstances.
If something "feels funny", there are a few things you can do. One, write down all the reasons they could act this way and choose the most believable one. (It should never be "because I need it to happen for the plot"). Two, you could revise the way the characters are acting so it makes more sense, even if it takes the plot in a different direction. Or three, you could call up your writing buddy (more on this later) and ask them if they think it makes sense. A fresh set of eyes can go a long way in fixing mistakes in your story.
4. Develop the relationship s-l-o-w-l-y.
If your characters meet on the page, chances are they're going to be apprehensive at best and hate each other at worst. Either way, people don't immediately become best friends, especially if they're very different people. It takes time and circumstance to form a close bond with someone.
People don't grow close overnight most of the time (no dirty meaning intended). Some of the best relationships come out of periods of hardship and trauma, or conflict between the two parties involved. Other times, it'll be a few chapters before your characters realize how much they actually have in common. Either way, you need to create tension so the reader roots for the relationship to happen and benefit both characters.
One way to do this is to actually make characters the reader wants to love. For example, it's much easier to sympathize with Pearl and Amethyst's conflict in Steven Universe, once you understand how much pressure Pearl was under while living on Homeworld and trying to conform with the Diamonds' expectations for her. Meanwhile, Amethyst has never known the sort of life that Pearl did, and is much more apt to breaking the rules for pleasure. This causes them to butt heads often, especially given their other personality differences (such as Pearl being a J and Amethyst being a P).
Another thing to do is to dangle the chance for a relationship right in front of the reader's eye. This takes a lot of practice, but it usually involves the characters resolving that believable conflict before...ah, shucks, John said something insensitive to Linda and now they don't think they can stay friends. Remember to balance conflict and success, though. You don't want frustrated readers.
5. Relationships change people.
Relationships can make people better, or they can make them worse. Either way, the person will almost never stay the same after the relationship either concludes or reaches the end of its arc. One of the best examples I can think of is how Shadow Weaver interacted with her four apprentices in She-Ra over the course of her life when they were teenagers. Catra, Adora, and Glimmer either became worse people or less healthy with her in their lives. Either way, none of them walked away from her the same way they were before. (And we can't forget how Light Spinner's relationship with Micah changed her, too. Who spares someone when they're insane, unless they love them?)
That's what people writing relationships need to strive for. Bad relationships make people worse, as any traumatic event does. Maybe you won't repeat the cycle of abuse if you find yourself in that situation, but you will walk away less healthy than before. Do your research on these sorts of relationships, and figure out what works best for your character. You may not explore all of it in the same book as the relationship's end or stagnation point, but you should have a general idea of how it affects them.
If you want to frame a relationship as good, show how the characters' flaws and strengths complement each other. Maybe the carefree, reckless boy meets a stern, responsible girl and has to learn to be wiser and less dangerous in order to win her heart. And maybe the girl learns through his love to loosen up a bit and have more fun. If you want, you can make a list in your journal of each character's strengths and weaknesses (any sort - physical, social, mental, emotional). Then do a "butterfly line" where one character's strength can teach the other to overcome their weakness.
And remember lastly that all of this takes practice. It's impossible to write a compelling relationship on your first try - I've been writing since I was eight, and I still have to rework my characters' interactions with pretty much each draft. Don't sweat it too much - write, listen to feedback, and observe the relationships found in good stories. In the next chapter, I'm going to detour a bit on romance, since that's a separate topic that deserves its own place to shine.