A kézikönyv részletes.

In Hungarian, the present-tense verb to be is often left out in simple third-person statements when the predicate is a noun or an adjective.

So:

• A kézikönyv részletes. = The manual is detailed.

Literally, it looks like The manual detailed, but Hungarian grammar allows that.

Compare:

• Én részletes vagyok. = I am detailed.
• Te részletes vagy. = You are detailed.
• A kézikönyv részletes. = The manual is detailed.

In the third person singular, the is part is normally not spoken here.

A is the definite article, meaning the.

Hungarian has two forms of the definite article:

• a
• az

Which one you use depends on the sound at the beginning of the next word:

• a before most consonant sounds
• az before vowel sounds

So:

• a kézikönyv = the manual
• az asztal = the table

Since kézikönyv starts with the consonant sound k, the correct form is a.

Because here részletes is not directly modifying the noun inside the noun phrase. It is the predicate adjective.

There is an important difference:

• A kézikönyv részletes. = The manual is detailed.
• A részletes kézikönyv = the detailed manual

So:

• after the noun: it means is detailed
• before the noun: it means detailed manual

This is very similar to the difference in English between:

• The manual is detailed
• the detailed manual

Yes, kézikönyv is one word. Hungarian often writes compounds as a single word.

It is made up of:

• kézi = hand / manual / by hand
• könyv = book

So the literal idea is something like handbook, and in actual use it commonly means:

• handbook
• manual

In this sentence, manual or handbook both fit well, depending on context.

It does not change for gender, because Hungarian has no grammatical gender like he/she agreement in adjectives.

So there is no difference like:

• detailed for masculine
• detailed for feminine

Hungarian just uses the same adjective form.

For number, predicate adjectives can change in the plural:

• A kézikönyv részletes. = The manual is detailed.
• A kézikönyvek részletesek. = The manuals are detailed.

So in your sentence, részletes stays singular because kézikönyv is singular.

A rough English-friendly pronunciation is:

aw KAY-zee-kurnyv RAY-sleh-tesh

A few important details:

• á/é/í/ó/ú/ő/ű and other accents matter in Hungarian; they are not optional
• é is a long vowel, roughly like ay in say, but cleaner and more stable
• ö is like German ö or French eu; English does not have an exact match
• ny is like ny in canyon or Spanish ñ
• sz sounds like English s
• s by itself sounds like English sh

So:

• kézi begins with a long ké
• könyv has the ny sound
• részletes contains sz = s sound, but the final s sounds like sh

That final word is roughly:

• részletes ≈ RAY-sleh-tesh

This word order is the most neutral and natural one for a basic statement:

• A kézikönyv részletes.

Hungarian word order is more flexible than English, but changing it usually changes the emphasis.

For example:

• A kézikönyv részletes. = neutral: The manual is detailed.
• Részletes a kézikönyv. = puts more focus on detailed, something like The manual is detailed or It’s detailed, the manual is.

So yes, other orders are possible, but they are not all equally neutral.

It most directly means detailed, but depending on context it can also suggest:

• thorough
• comprehensive
• elaborate

For example, a részletes kézikönyv is a manual that gives a lot of information and explanation.

So if the meaning shown to you was The manual is detailed, that is a very good basic translation, but the exact English word may vary a little depending on context.