Il pescivendolo pesa il salmone e mi dà lo scontrino.

Pescivendolo means fishmonger or fish seller.

It is built from:

• pesce = fish
• vendere = to sell

So a pescivendolo is literally someone who sells fish.

A learner may also notice that this is a very Italian kind of compound noun: instead of saying something like fish seller, Italian often has one single word.

Il is the masculine singular definite article, meaning the.

So:

• il pescivendolo = the fishmonger

Italian usually uses articles more often than English does, so where English might sometimes say just fishmonger in certain contexts, Italian normally wants the article: il pescivendolo.

Pesa is the third-person singular present tense of pesare = to weigh.

The subject is il pescivendolo, which is he in meaning, so the verb must match that subject:

• io peso = I weigh
• tu pesi = you weigh
• lui / lei pesa = he / she weighs

So:

• Il pescivendolo pesa il salmone = The fishmonger weighs the salmon

In this sentence, pesa can naturally mean either weighs or is weighing, depending on context.

Italian often uses the simple present where English might use either:

• The fishmonger weighs the salmon
• The fishmonger is weighing the salmon

If you really want to stress the ongoing action, Italian can also use:

• sta pesando = is weighing

But in everyday Italian, the simple present pesa is very normal.

Here il salmone refers to a specific piece or portion of salmon being handled in the shop, so Italian uses the definite article:

• il salmone = the salmon

Italian often uses the definite article with direct objects when the thing is understood as specific in the situation.

A more generic statement could also use the article:

• Il salmone è costoso = Salmon is expensive / The salmon is expensive

So articles with food words in Italian do not always work exactly like English.

Mi means to me. It is an indirect object pronoun.

So:

• dà = he/she gives
• mi dà = he/she gives to me

In the sentence:

• mi dà lo scontrino = he gives me the receipt

Italian usually puts these object pronouns before the conjugated verb:

• mi dà
• ti dà
• gli dà
• ci dà

English puts me after the verb, but Italian does not.

The accent distinguishes the verb dà from the preposition da.

• dà = he/she gives from dare
• da = from, by, at

So in this sentence:

• mi dà = gives me

The accent helps avoid confusion in writing.

Italian uses lo instead of il before certain masculine singular words, including words beginning with:

• s + consonant
• z
• ps
• gn
• and a few others

Since scontrino begins with sc-, and that is s + consonant, you use:

• lo scontrino

Compare:

• il libro
• lo studente
• lo zaino
• lo scontrino

So:

• mi dà lo scontrino = he gives me the receipt

Grammatically, yes, but it would usually sound marked or emphatic.

The normal way is:

• mi dà lo scontrino

If you say:

• dà a me lo scontrino

it sounds more like:

• he gives the receipt to me
  with special emphasis on to me.

In ordinary speech, Italian strongly prefers the pronoun form mi here.

Because short object pronouns like mi, ti, lo, la, gli, ci, vi normally come before a conjugated verb.

So:

• mi dà = correct
• dà mi = not correct in standard Italian

This is a very important pattern in Italian:

• mi parla = he speaks to me
• ti vede = he sees you
• lo compra = he buys it

So in your sentence, mi must go before dà.

A couple of points may help:

• In scontrino, the sc before o is pronounced like sk, not like English sh.
  So it sounds roughly like skon-TREE-no.

• In pescivendolo, the sc before i is pronounced like sh.
  So that part sounds roughly like PESH-ee...

Very roughly:

• pescivendolo ≈ peh-shee-VEN-do-lo
• scontrino ≈ skon-TREE-no

That contrast is common in Italian:

• sc before e/i → like sh
• sc before a/o/u → like sk

It follows a very common Italian pattern:

Subject + verb + direct object + e + indirect object pronoun + verb + direct object

Breaking it down:

• Il pescivendolo = subject
• pesa = first verb
• il salmone = direct object
• e = and
• mi = indirect object pronoun, to me
• dà = second verb
• lo scontrino = direct object

So the sentence is nicely balanced:

• The fishmonger weighs the salmon and gives me the receipt.

This is a useful model for many everyday shop sentences in Italian.