The problem isn't really adjectives and adverbs, per se, it's just that they tend to weaken the writing. Any time you go for an adverb, you're using it to modify a verb, right? But really, if you found a better verb, it would be stronger.
He walked softly through the living room.
vs.
He tiptoed through the living room. or
He crept through the living room.
In the latter example, it's just a better verb, giving a more exact idea of what you're trying to imply. Tiptoeing has a different connotation from creeping, right?
So that's the issue with adverbs. (Actually, I hate when people harp on adverbs, because those aren't the problem. The problem is really the verbs themselves!)
For adjectives, they're just so easy to overdo. Middle school creative writing classes teach us to be flowery with our writing, and it took me AGES to get out of the habit to write things like, "The melodious songbird sat on the aging, brown tree branch that hung with green roping vines and BLAH BLAH BLAH." Your eyes are glazing over already, right? I read sentences like that and just want to yell, "A BIRD WAS ON A BRANCH. I GET IT."
Adjectives just weigh down your sentences, and usually, they're not necessary. If you say grass, people know it's green. If you say sky, people know it's blue. If you want to say it's a midnight blue so deep it seemed the stars pinned it in place, then it must reflect something about your character. (Romance on the brain, maybe?) There's a rule of thumb that you should only describe what the reader won't already assume.
Finally, the reason people say to use "said" all the time is that the brain ignores it. When you start using creative little ways to avoid it, the reader sees that word, and it can pull you out of the story. I wouldn't worry too much about changing the word said unless it's really, really necessary. A lot of times, your dialogue is going to get it across anyway. Like, if someone says, "Get your ass out here!" no one is going to assume that's being whispered.
I hope this helps! Good luck!