Mijn bril ligt op het nachtkastje naast het bed.

In Dutch, bril is normally a singular noun. It means glasses or a pair of glasses.

• mijn bril = my glasses / my pair of glasses
• twee brillen = two pairs of glasses

So this is a place where Dutch and English use different number patterns.

Because mijn is a possessive adjective: my. In Dutch, a possessive normally replaces the article.

So you say:

• mijn bril = my glasses
• de bril = the glasses

But not standard:

• de mijn bril
• het mijn bril

English works the same way: you say my glasses, not the my glasses.

Dutch often uses a posture verb to describe where something is located.

Common ones are:

• liggen = to lie
• staan = to stand
• zitten = to sit / be located in or attached to

For something like glasses resting on a surface, Dutch usually uses liggen:

• Mijn bril ligt op tafel.

English often just uses is, but Dutch is more specific here.

Ligt is the present tense, third-person singular form of liggen.

The subject is mijn bril, which is singular, so we use ligt:

• ik lig
• jij ligt / lig jij
• hij/zij/het ligt

So Mijn bril ligt... means My glasses are lying... / My glasses are...

Op means on or on top of. Since the glasses are resting on the surface of the bedside table, op is the natural preposition.

• op het nachtkastje = on the bedside table

If the glasses were inside a drawer, Dutch would use something like in instead:

• in het nachtkastje = in the bedside table / in the nightstand

Because nachtkastje ends in -je, which makes it a diminutive. In Dutch, diminutives are always het-words.

So:

• het kastje
• het nachtkastje

This is true even if the non-diminutive word is a de-word.

The ending -je is a diminutive ending. It often means small, little, or sometimes just sounds more natural in everyday speech.

• kast = cupboard/cabinet
• kastje = little cupboard / small cabinet
• nachtkastje = bedside table / nightstand

In many cases, the diminutive does not strongly mean tiny. It is simply the normal word people use.

Because bed is a neuter noun, so it takes het:

• het bed

You just have to learn whether a noun is a de-word or a het-word. Unfortunately, this is often something learners memorize noun by noun.

Also, after naast, Dutch normally still uses the article:

• naast het bed = next to the bed

Usually it is understood as describing the bedside table:

• the glasses are on the bedside table
• the bedside table is next to the bed

So the most natural reading is: My glasses are on the bedside table next to the bed.

In other words, naast het bed helps identify which nachtkastje we mean.

This sentence uses the normal Dutch main-clause order:

• Mijn bril = subject
• ligt = verb
• op het nachtkastje naast het bed = place information

So the basic pattern is:

subject + verb + rest

But Dutch also allows you to move the place phrase to the front for emphasis. Then the verb still stays in the second position:

• Op het nachtkastje naast het bed ligt mijn bril.

That is also correct, but it sounds more like you are emphasizing the location.