Necesito un pedazo de pan.

In Spanish, the subject pronoun is often omitted because the verb ending already shows who is doing the action.

• Necesito = I need
• The -o ending tells you it is yo.

So Necesito un pedazo de pan is perfectly natural.
You could say Yo necesito un pedazo de pan, but that usually adds emphasis, such as:

• Yo necesito un pedazo de pan, no ella.
  I need a piece of bread, not her.

Because pedazo is a masculine noun.

In Spanish, articles must match the gender of the noun:

• un for masculine singular nouns
• una for feminine singular nouns

So:

• un pedazo
• una pieza
• una rebanada

Even though the thing being referred to, pan, is also masculine, the article un is matching pedazo, not pan.

Here, de means of.

So the structure is:

• un pedazo de pan = a piece of bread

This is a very common Spanish pattern:

• un vaso de agua = a glass of water
• una taza de café = a cup of coffee
• un kilo de manzanas = a kilo of apples

The first noun tells you the amount or container, and de links it to the thing itself.

Because in this sentence, pan is being used in a general, uncountable sense: some bread, not a specific loaf.

• un pedazo de pan = a piece of bread

You would use an article if you meant a specific bread:

• un pedazo del pan = a piece of the bread
• un pedazo de un pan = a piece of a loaf of bread

So the version without an article is the normal way to say it when you just mean bread in general.

Yes, you could also say trozo. Both can mean piece or chunk.

• un pedazo de pan
• un trozo de pan

Both are understandable and natural. Depending on context, trozo can sometimes sound a bit more neutral, while pedazo can sometimes suggest a larger or more noticeable piece. But in many everyday situations, they overlap.

For bread specifically, other possibilities may also appear depending on what kind of piece you mean:

• una rebanada de pan = a slice of bread
• un trozo de pan = a piece of bread
• un pedazo de pan = a piece/chunk of bread

Use rebanada when you mean a slice specifically.

• una rebanada de pan = a slice of bread

Use pedazo when you mean a more general piece, not necessarily a neat slice.

For example:

• If bread has been cut evenly, rebanada is likely better.
• If someone tears off some bread by hand, pedazo sounds more natural.

So pedazo is broader, while rebanada is more specific.

They are different.

• Necesito = I need
• Quiero = I want

So:

• Necesito un pedazo de pan means you need it.
• Quiero un pedazo de pan means you want it.

In real life, people sometimes use quiero in shops or restaurants, but in Spain it can sound a bit direct depending on tone. Politer options include:

• Quería un pedazo de pan = I wanted a piece of bread
• Me gustaría un pedazo de pan = I would like a piece of bread

But if the intended meaning is truly need, then necesito is correct.

A simple pronunciation guide for Spain Spanish is:

• Necesito → neh-seh-SEE-toh
• un → oon
• pedazo → peh-DAH-thoh
• de → deh
• pan → pahn

In much of Spain, the z in pedazo is pronounced like the th in think:

• pedazo → peh-DA-tho

That is one of the noticeable differences between Spain Spanish and most Latin American varieties, where z is usually pronounced like s.

Spanish often does not need a separate word equivalent to English some in this kind of phrase.

English:

• I need some bread
• I need a piece of bread

Spanish commonly says:

• Necesito pan = I need bread
• Necesito un pedazo de pan = I need a piece of bread

The idea of an unspecified amount is often understood without adding a special word. If you want to be more explicit, you can sometimes use:

• algo de pan = some bread
• un poco de pan = a little bread

But in this sentence, un pedazo de pan already gives the quantity.

Yes. Pedazo literally means piece, but it can be used in other ways too.

Common literal use:

• un pedazo de pan = a piece of bread

It can also be used more expressively in Spanish, sometimes to mean something like huge bit or even as emphasis in informal speech. For example, in some contexts pedazo de can intensify what comes after it.

But in your sentence, it is just the normal literal meaning: piece.

Yes. Necesito pan is grammatically correct and natural.

The difference is:

• Necesito pan = I need bread
• Necesito un pedazo de pan = I need a piece of bread

The second one is more specific about the amount. If you only want a small portion, un pedazo de pan is clearer.

Here is the breakdown:

• Necesito — verb, first person singular present of necesitar
• un — indefinite article, masculine singular
• pedazo — noun, masculine singular
• de — preposition
• pan — noun, masculine singular

So the structure is:

verb + article + noun + preposition + noun

That pattern is extremely common in Spanish.