I want to improve my skills in writing and feel the best way to do that is to do character studies on my favorite characters. How do I go about doing that?

What works for me is looking up certain characters on FANDOM; going over their depictions, personalities, appearances, etc. It really helps when you’re trying to make fictional characters of your own design

7884732 That's a bad way to go about it. You should have been studying the story structures, not the characters. The characters are just tools for the story.

7884749
When say story structure you mean the 7 basic plots?

7884834 That's part of it.

When you read a good story, it's not enough that you just feel good about it. Figure out what made it good. What were those elements that made it shine? Once you are able to figure that out, you'll be able to recreate it in your own stories. And in time, you'll figure out new elements that make your own stories shine.

As an example, you'll figure out that characters are used to tell a story. It's not the other way around. The story shouldn't be used to circle-jerk characters. So, when you start the process with characters, it's like building a roof of your house before you even start on the foundation. You're doing it wrong.

7884903
I don't disagree with this sentiment, but I usually approach stories from characters first as I consider the "story" as the parts of a character's life that I am interrupting. My usual starting point is asking "Does this character have an interesting story to tell?" and I go from there. In my narrative construction, characters are the foundation, and it's up to me as the author to discover if they have a story worth telling and build it out. It might be a difference in just how we conceptulize a story to arrive at the same conclusion though, admittedly. I don't want to go further than that though since it's outside the scope of the question.

As far as studying the characters, looking through wikipedia articles and episode transcripts can help you figure out how they talk and interact with others, but it's not so important when developing them how you will be realizing them in your stories. If you're just starting out, I don't see an issue with using a few shortcuts and tricks to get going. I've seen a few writers discount the idea of things like "character sheets" to develop your characters, but especially when starting out, I don't see a problem with the practice as long as you realize that it's not an end-all, be-all document. You'll discover more about the characters as you write your story, and that's perfectly fine. I try talking to them, placing them in various scenarios to see how they might deal with a problem, and other mental exercises to realize who they are. After all, I need to get to know who they are first before the reader is able to do the same.

Also, be sure to consider that characters in your stories are intrinsically just extensions of yourself no matter how much you study and prepare them. One of the important things is to be able to understand them and their motivations as even if you know what they are doing is right or wrong, they should be able to rationalize their actions within their own worldview rather than your own. I always say that "empathy" is my secret sauce to making my stories. I always ask what the character wants to do and how that aligns or misaligns with the story I want to tell. That tension between me as the author and the character as an actor can be a good source of conflict.

If you want a broad picture try TvTropes. Plug "Mlp friendship is magic Tv Tropes" into google.

Pick a character. Read about them. Read the tropes people have applied to them. Remember that is unlikely to build a fleshed out character by the ttropes first*. the character came first the tropes are viewers impression.

Watch the character afterwards and see how the tropes correlate to the character. See if an individual episode has different tropes. Look at their motivations ect...

*The only exception I can think of is Darth Vader. In a New Hope Lucas had a short checklist and Vader fit the bill. It is why Obi Wan called him Darth like it was his first name (it might have been at that point). He was an unimportant (setting wise) cog in the imperial military. He was made to be a villain for Luke to strive to overcome. The rest all came later...

Keep in mind how I build a character is much different from hos to study a character. And some narrative structures do put them on the back burner...