TL;DR Japanese doesn't really have adjectives. Everything you think of as an adjective is a verb-phrase (a tiny sentence inside the real sentence). This is great because you can put any verb-phrase in front of a noun to add simple or extremely complex descriptions to the noun. That's the only way to add descriptions to nouns in Japanese grammar. Thinking of it like gets rid of all of the exceptions and weird coincidences and reduces the number of rules you have to learn.
Japanese teachers and text books usually talk about 2 types of adjectives in Japanese but I find this confusing and more complicated than it needs to be.
First, let's start with the advanced stuff. How do you say something complicated like "a person that is riding a horse"? Now for an english speaker, this sentence doesn't have any adjectices, so why is it relevent? It's relevant because it's still a noun and something that describes the noun. It's the most general case, you can use it for the simplest and the most complex descriptions. You can say "a red person" in English but you can also switch that to "a person that is red". Anything you can do with an adjective you can do with "... that is ...". So, how do you say "a person that is riding a horse" in Japanese? It's 「馬に乗る人」. You just take the verb-phrase 「馬に乗る」 - "riding a horse" and put it in front of the noun. In English this is a bit like "a riding-a-horse person". You can do more complex things in English like "a riding-a-horse-and-eating-ice-cream person" but it gets weird and you'll probably want to switch to "a person that is riding a horse and eating ice cream". In Japanese, there's only one way it's 「馬に乗ってアイスを食べる人」. You can put the most complex verb-phrase in front of the noun and that's just how Japanese works.
So for Japanese you describe nouns by putting a verb-phrase in front but this is "advanced" grammar. Before textbooks teach you that, they will teach about い and な adjectives and you will be confused but really, both of these are just verb-phrases that go in front of a noun. I think they only get called adjectives because somebody thought "first we teach nouns, then verbs, then adjectives, then adverbs, then blah blah ... and eventually verb-phrase+noun". It's also partly because they always teach です before they teach だ to be polite. The result is the horrible confusion that is い and な adjectives.
First problem, い-adjectives can be in the past tense. WTF? How can an adjective have a tense? In fact い adjectives behave exactly like any verb in Japanese, you can make a sentence with them - 「道路が広い」 - "the road is wide". That's valid sentence. There's no other verb there. It's not like leaving out the subject in Japanese. The subject is often omitted in Japense but you can always put it back in if you like and the sentence is still correct. There is no missing verb you can put back in to 「道路が広い」, that's the whole sentence right there. You can put a です at the end to make it polite but if you were creating an impolite sentence, you couldn't put a だ in. You can even put it in the past tense - 「道路が広かった」 - "the road was wide" by conjugating the... adjective? no the verb. The verb is "to be wide" which is a bit weird for English speakers but it's not awful.
So, if it works exactly like a verb, it's a verb! If you insist that it's an adjective then you have to also explain that adjectives in Japanese have a past tense and a て form and also that Japanese has sentences with no verb sometimes.
Now let's see how it's usually introduced, as an い adjective. 「広い道路」 - "wide road". If you think of 広い as a verb then this is just a verb-phrase in front of a noun, that's not a new rule, you already knew that. 「広かった道路」 - "road that was wide" is quite natural now. It's definitely a bit weird that Japanese has a verb "to be wide" but that's a lot less weird than having adjectives with tense. "is-wide road" and "was-wide road" are the direct translations into English. You wouldn't say them but they kind of work.
So next is な adjectives. It turns out that な is actually だ in disguise. It gets pronounced な when you say it before a noun. Try saying だ instead, it's a bit awkward, so maybe that's why it morphed. So 「きれいな人」 - "a beautiful person" is really 「きれいだ人」and this becomes really obvious when you want to say "person that was beautiful" because it's 「きれいだった人」. Look at that, だった is the past tense of だ, that's not a new rule either! 「きれいだ」- "it's beautiful", 「きれいだった」 - "it was beautiful". So all we have here is just another verb-phrase in front of a noun. "an is-beautiful person", "a was-beautiful person" are the direct translations into English, again weird but they make sense.
So if I was teaching Japanese I would say that everything about adjectives and decribing nouns in Japanese can be summed up as
- put any verb-phrase in front of a noun to add more detail, e.g. "an X that Y" in English is just 「Y X」 in Japanese.
- there is a verb "to be wide" in Japanese and "to be blue" and lots more and they all end in い (and they behave just like every other verb in Japanese)
- when it comes before a noun, だ turns into な
Compare that with
- There are 2 types of adjectives in Japanese, い and な adjectives.
- Adjectives in Japanese have tenses... seriously
- the past tense of an い adjective is made by blah blah (oh weird, that's a lot like verbs but let's pretend we didn't notice that)
- the past tense of a な adjective is made by blah blah (oh weird, that's the same as だ but we didn't learn だ yet because that's not polite!)
- Adjectives in Japanese also have a て form, just like verbs.
- In fact, pretty much anything else about verbs applies to adjectives, negation etc.
- Unlike English, not all sentences in Japanese have a verb, sometimes they just end in an い adjective.
- If you want to make a sentence out of a な adjective, you just replace な with だ unless (or drop it completely if you're using です)
- put any verb-phrase in front of a noun to add more detail, e.g. "an X that Y" in English is just 「Y X」 in Japanese.
My way is just 3 very simple points. The standard way is so much more complicated, full of exceptions and coincidences that you're supposed to ignore.