-i adjectives are the like the first ones you listed. the -i changes to -ku to make an adverb, -kunai for "isn't ...", -katta for "was ...", -kunakatta for "wasn't ..." etc.
na adjectives do not do this and you must change the desu at the end to change the tense or negate it. (If someone knows if there's an equivalent to the -i adjective ...-ku for -na adjectives, I'd like to know that). Also, when using -na adjectives before a noun, you must put na between them.
Example:Kore wa shizuka na neko desu.
If anyone can add to this or if something needs to be uhh, corrected, please do.