Alright, team, let's go through this again!

HYPHEN
a hyphen connects compound adjectives before a noun. "a twenty-five-year-old man," "a state-of-the-art security system," etc. https://twitter.com/Thrawn589/status/1381389481207603200

you do not do this with -ly adverbs. you do not write "a perfectly-suitable house," for example. it's "a perfectly suitable house."

in addition to that, hyphens connect compound words, such as a check-in, a free-for-all, etc.

EN-DASH
an en-dash, slightly longer than a hyphen, is used for numbers only. so, date ranges, temperatures, times.

"the 2011–2012 season was the best for that football team."
"read chapters 4–6 before our next class."
"bake 8–10 minutes until golden along the crust."

HOWEVER, if your sentence includes "from" or "between," don't use an en-dash. use "to."

"she played D&D from 2019 to 2025," not "she played D&D from 2019–2025."

em-dash
an em-dash, the longest, is arguably the most versatile. it takes the place of commas, colons, semicolons, and parentheses.

"sadie wanted to write a deneith—a dragonmarked character from the eberron setting with themes of protection and defense." (instead of a comma)

"sadie painted the wall in her favorite color—teal." (instead of a colon)
"sadie was trying to buy a house—something she hadn't done before—while also doing a lot of freelance work." (instead of parentheses)

in most cases, the em-dash is considered "less formal" than what it's replacing. it's less formal than the parentheses and colon. it's also more intrusive, especially when replacing parentheses.

you can also use them to omit part of a word:
"bloody he—" yvaine shouted.

or to end a letter or a tweet thread:

— sadie lowry