May isang baso ng malamig na tubig sa lamesa.

Here, may introduces existence. It works a lot like English there is or there are.

So:

May isang baso ng malamig na tubig sa lamesa.
= There is a glass of cold water on the table.

A very common pattern is:

May + thing + location

So in this sentence:

• may = there is
• isang baso ng malamig na tubig = a glass of cold water
• sa lamesa = on the table

Filipino often does not need a separate copula like English is/are in sentences like this.

In English, you need there is.
In Filipino, may already carries that existential idea, so no extra word for is is needed.

That is why May isang baso... is already a complete sentence.

Isang is the form normally used before a noun.

It is basically isa plus the linker -ng:

• isa = one
• isang baso = one glass / a glass

So isang baso is the natural way to say one glass or a glass.

This is the normal way to say glass of cold water.

• baso = glass
• ng links it to what it contains
• malamig na tubig = cold water

So baso ng tubig literally means glass of water.

In this kind of phrase, ng often corresponds to English of:

• isang tasa ng kape = a cup of coffee
• isang bote ng gatas = a bottle of milk
• isang baso ng tubig = a glass of water

Filipino adjectives normally use a linker before the noun they modify.

Here:

• malamig = cold
• tubig = water
• malamig na tubig = cold water

Because malamig ends in a consonant, the linker appears as the separate word na.

So:

• malamig na tubig = cold water

If the first word ended in a vowel or n, the linker is often attached as -ng instead.

In baso ng malamig na tubig, malamig describes tubig, not baso.

So the meaning is:

• a glass that contains cold water

It does not primarily mean that the glass itself is cold.

That is an important difference in structure:

• baso ng malamig na tubig = glass of cold water
• malamig na baso ng tubig = a cold glass of water, where malamig more directly modifies the whole phrase or may suggest the glass/drink is cold

That is the most natural neutral word order for an existential sentence like this.

A common pattern is:

May + thing + location

So:

• May isang baso ng malamig na tubig sa lamesa.

This sounds natural and straightforward.

You can move the location for emphasis, for example:

• Sa lamesa, may isang baso ng malamig na tubig.

But the original order is very common.

After may, Filipino usually uses a simple location phrase with sa.

So:

• May isang baso ... sa lamesa.

If you use nasa, that usually fits a different sentence pattern where the location itself is the predicate:

• Ang baso ay nasa lamesa. = The glass is on the table.

So both can talk about location, but they belong to different sentence structures:

• May ... sa ... = There is ...
• Ang X ay nasa ... = X is at/on/in ...

Sa is a general location marker. Depending on context, it can correspond to English in, on, at, or to.

In this sentence, sa lamesa is understood as on the table because that is what makes sense with table.

So:

• sa bahay = at home / in the house
• sa mesa = on the table / at the table
• sa paaralan = at school

The exact English preposition depends on context.

Often, yes.

All of these can express existence:

• may
• mayroon
• meron

But may is the most straightforward and common choice before a noun phrase, especially in simple sentences like this:

• May isang baso ng malamig na tubig sa lamesa.

You may also hear:

• Mayroong isang baso ng malamig na tubig sa lamesa.
• Merong isang baso ng malamig na tubig sa lamesa.

Those are understandable, but may is especially natural here.

Yes. That is a very common point of confusion for learners.

May can express:

• existence: there is / there are
• possession: has / have

Compare:

• May isang baso sa lamesa. = There is a glass on the table.
• May baso ako. = I have a glass.

So the meaning depends on the structure of the sentence.
In your sentence, may is existential because it introduces something that exists in a location.

It can mean either one glass or a glass, depending on context.

In many sentences like this, isang baso is naturally understood as indefinite, like English a glass.

So:

• isang baso = a glass / one glass

If the speaker wants to emphasize the number one, context or intonation will make that clearer. Otherwise, it often simply introduces a single item.

Yes. You would usually use mga for plurality.

For example:

• May mga baso ng malamig na tubig sa lamesa.
  = There are glasses of cold water on the table.

If you want to be more specific about the number, you can also say:

• May dalawang baso ng malamig na tubig sa lamesa.
  = There are two glasses of cold water on the table.

So the same basic pattern stays the same: May + noun phrase + location