I've just found the key to writing Sesame Street characters! OK so, this may seem obvious to some, but the key is, the characters are totally innocent. They may not be totally void of occasional sarcasm and they get physically exhausted, but they are completely void of cynicism. They live in their own little worlds, have they're personalities and beliefs, but none of them are tainted by the world. They may get upset sometimes, and unfortunate things like bullying, death, or racism may occur, but they always remain wide-eyed, curious, and ambitious. They don't have a cynical bone in their bodies. Once I figured that out, it made it much easier for me to come up with stories for them, and write them in an accurate way.
When it comes to the characters, I sort them on a piece of paper and separate them into sections. How I write and how other people write vary. I've been writing for almost ten years(not on here) so I think the more you write, the better understanding you'll have which helps you grasp things like the storylines, characters, subplots, etc.
My sister and I once came up with a thing we called "20 Simple Rules for Writing Fanfiction."
1. Know Your Show. If you don't know it, research it, or don't attempt to write it.
2. Original Characters are fine, just be careful when using them.
3. When doing song fics, DO NOT USE THE SAME STINKIN' SONG TEN TIMES IN ONE STORY!
4. When collaborating with another writer, make SURE you know what the other writer likes.
5. If you can make crossovers work, go for it. If one fandom overshadows another too much, watch it.
6. Don't make OC's uber "speeeeshul" (spelling intentional). Readers will end up reading about them instead of the canon characters
7. Don't use the same stuff over and over again in every single stinkin' story!
8. When creating OC's, make sure there isn't a canon character with the same name in the fandom.
9. Write what you want to write. Don't worry about pleasing others.
10. Don't be afraid to use a little imagination. Think outside the box. Get unrealistic sometimes.
11. K.I.S.S. Keep It Simple, Stupid!
12. When putting in a subplot, make sure it fits with the rest of the story, and the two plots can be tied together. Don't put a subplot into a story so you can stick a character in there, just for the sake of he/she being in the story. Don't use certain characters if they don't fit.
13. Research topics you're not sure how to write for.
14. Love interests are fine, especially if the character you want to give a love interest to doesn't have one to begin with. However, be careful when creating a love interest for a character who has a significant other (especially if they're married).
15. Give credit where credit is due.
16. Remember you can NOT copyright a name, or a nickname. If you decide to name your character "Fred," and you see another author's story using a character named "Fred," you should not whine and throw a hissy fit saying that you own the name and nobody can ever use it again.
17. Always, always, ALWAYS spell check and proofread your stories.
18. Never use the Caps Lock of Death when writing an entire story. It's okay to use it for one or two lines of dialog to show how mad someone is, but not for an entire story!
19. DO NOT DICTATE TO OTHERS WHAT TO WRITE!!!!
20. Keep the character in character as much as possible. A little out of characterness is fine if you want to add a little angst and drama to your story, just try not to go overboard.