На книжной полке лежит мой словарь.

Because after на meaning on in a location sense, Russian uses the prepositional case.

The basic form is:

• книжная полка = a book shelf / bookshelf shelf

  But after на for location, it changes to:

• на книжной полке = on the bookshelf / on the shelf

Both words change because книжная is an adjective modifying полка:

• книжная полка → nominative
• книжной полке → prepositional

A very useful rule:

• на + prepositional = location, on / at
• на + accusative = motion toward, onto / to

So:

• На книжной полке лежит мой словарь. = My dictionary is lying on the bookshelf.
• Я кладу словарь на книжную полку. = I put the dictionary onto the bookshelf.

Книжной is a form of the adjective книжный, which comes from книга meaning book.

So:

• книга = book
• книжный = book-, book-related
• книжная полка = book shelf / bookshelf

In this sentence, книжной is just the case form required by на ... полке.

Лежит literally means lies or is lying.

Russian often uses different verbs for where something is positioned:

• лежать / лежит = to lie, to be lying
• стоять / стоит = to stand, to be standing
• висеть / висит = to hang, to be hanging

A dictionary on a shelf is often imagined as lying flat, so лежит sounds natural.

English usually just says is, but Russian often prefers a more physical verb showing position.

Yes, if the dictionary is standing upright like a book in a row.

Compare:

• На книжной полке лежит мой словарь. = My dictionary is lying on the shelf.
• На книжной полке стоит мой словарь. = My dictionary is standing on the shelf.

So the choice depends on how the object is positioned, not just what it is.

In modern Russian, the present tense of to be is usually not stated.

So Russian often says things like:

• Мой словарь на книжной полке. = My dictionary is on the shelf.

In your sentence, though, the main verb is not to be but лежит = is lying. So Russian gives more detail than English often does.

Because мой словарь is the subject of the sentence, so it stays in the nominative case.

• словарь = dictionary
• мой = my

мой agrees with словарь in:

• gender: masculine
• number: singular
• case: nominative

So:

• мой словарь = my dictionary

If the dictionary were in another case, both words could change:

• нет моего словаря = there is no my dictionary / I don’t have my dictionary
• вижу мой словарь or more commonly вижу свой словарь = I see my dictionary

Yes. A noun ending in -ь can be either masculine or feminine, so you have to learn its gender.

словарь is masculine, which is why it takes:

• мой словарь
• новый словарь

Some other masculine nouns ending in -ь are:

• день = day
• учитель = teacher
• рубль = ruble

So the soft sign -ь does not automatically mean feminine.

Because the subject, мой словарь, is singular.

Russian verbs in the present tense agree with the subject in number and, in past tense, also in gender.

Here:

• мой словарь = singular
• therefore лежит = singular

If it were plural:

• На книжной полке лежат мои словари. = My dictionaries are lying on the shelf.

Yes. Russian word order is flexible, although different orders can shift emphasis.

Your sentence:

• На книжной полке лежит мой словарь.

This naturally focuses first on the location, then tells you what is there.

You could also say:

• Мой словарь лежит на книжной полке.

That starts with my dictionary and sounds more like you are talking about the dictionary and saying where it is.

Very roughly:

• На книжной полке лежит мой словарь. = On the shelf is my dictionary.
• Мой словарь лежит на книжной полке. = My dictionary is on the shelf.

Both are correct.

Literally, yes, на often means on. But in real usage, на полке can simply mean on the shelf in the normal sense of being placed on one of the shelf surfaces.

So in English, depending on context, it may be understood as:

• on the shelf
• on the bookshelf
• on one of the shelves

Russian does not necessarily force a distinction here.

Russian has no articles like English a and the.

So whether something is a dictionary or the dictionary is understood from context.

In this sentence:

• мой словарь already means my dictionary, so that is specific enough.
• на книжной полке can mean on a bookshelf, on the bookshelf, or on the book shelf, depending on context.

This is very normal in Russian.

The stress is:

• На кнИжной пОлке лежИт мой словАрь.

Word by word:

• на
• кнИжной
• пОлке
• лежИт
• мой
• словАрь

A rough English-style approximation would be:

• na KNIZH-nay POL-kye lye-ZHEET moy sluh-VAR’

But it is best to learn the real Russian sounds rather than rely too much on English approximation.