When the noun follows the -な adjective, -な is kept.
真面目まじめな人ひと。A serious person.

When the adjective is separated from the subject by a verb, -な is deleted.
彼かれは真面目まじめだ。He is serious.
彼かれは真面目まじめな人ひとだ。He is a serious person.  

The conjugation of -な adjectives is almost the same as that of nouns :

"(Someone) likes (something)", is translated in Japanese by "(someone) は (something) が 好すきです"。 Indeed, to like is translated by 好すき(な), a -な adjective.
私わたしはマンガが好すきだ。I like manga.

"(Someone) who likes (something)" is translated by "(something) が好すきな (someone)".
マンガが好すきな人ひと。A person who likes manga.
マンガが好すきじゃない人ひと。A person who does not like manga.
マンガが好すきだった人ひと。A person who loved manga.
マンガが好すきじゃなかった人ひと。A person who did not like manga.

Adjectives in -い always end with an い written in hiragana :
今日きょうは暑あつい。Today it's hot.
猫ねこは可愛かわいい。Cats are cute.

Some adjectives in -な end in い like 綺麗きれい(な)、有名ゆうめい(な) etc.

Generally, adjectives in -な are written in kanji and they do not have okurigana (kanas needed for conjugation), 嫌きらい(な) is the only exception.

When an -い adjective qualifies a noun, it directly precedes the name.
今日きょうは寒さむい日ひだ。Today is a cold day.
東京とうきょうは大おおきい町まちだ。Tokyo is a big city.

The conjugation of -い adjectives is different from that of -な adjectives.
Note that だ cannot be added to -い adjectives..

Note the exception : 良い・よい well, good (≠ food).