Il fioraio dice che il girasole dura più a lungo se cambi l’acqua ogni giorno.

Italian usually uses the definite article more often than English. Il fioraio means the florist.

Here, il fioraio is the subject of the sentence, so the article sounds natural and complete.
Also:

• fioraio = florist (masculine singular)
• fioraia = florist (feminine singular)

So Il fioraio dice... is simply The florist says...

Che here means that and introduces a new clause.

So:

• dice = says
• che il girasole dura più a lungo... = that the sunflower lasts longer...

This is very common in Italian after verbs like:

• dire che = to say that
• pensare che = to think that
• credere che = to believe that

English often drops that, but Italian usually keeps che.

Italian often uses the definite article with nouns when speaking about something specific or about a thing in a general, class-like way.

So il girasole can mean:

• the sunflower in this situation, or
• a sunflower as a type of flower being discussed

English is more flexible about dropping the article, but Italian usually keeps it here.

Dura comes from the verb durare, which means to last or to endure.

So:

• il girasole dura = the sunflower lasts

In this sentence, it refers to how long the flower stays fresh.

A few forms of durare:

• durare = to last
• dura = it lasts
• durano = they last

Because più a lungo is an adverbial expression meaning for longer or longer in the sense of duration.

• lungo by itself is usually an adjective meaning long
• a lungo functions like for a long time
• più a lungo = for a longer time / longer

So:

• una strada più lunga = a longer road
• durare più a lungo = to last longer

In this sentence, we are describing how long the flower lasts, so the adverbial expression is needed.

Because cambi is the tu form of cambiare in the present tense:

• io cambio
• tu cambi
• lui/lei cambia

So se cambi l’acqua ogni giorno means if you change the water every day.

Italian often leaves out the subject pronoun, so tu is understood but not stated:

• se cambi... = if you change...

If it were se cambia, it would usually mean:

• if he/she changes
• or in some contexts if one changes

It looks like one, but here it is functioning as the present indicative.

That can be confusing because for many -are verbs, some subjunctive forms look identical to other forms. For cambiare:

• tu cambi = present indicative
• che io cambi / che tu cambi / che lui cambi = present subjunctive forms

But after se meaning if in a real, possible condition, Italian normally uses the indicative, not the subjunctive:

• se cambi l’acqua... = if you change the water...

So in this sentence, think of cambi as the normal tu present form.

Because acqua is feminine singular, so it normally takes la:

• la acqua

But Italian does not like that vowel clash, so la becomes l’ before a vowel. This is called elision:

• la + acqua → l’acqua

You see this often:

• l’amica
• l’ora
• l’idea

Because ogni already means every, so no article is needed.

• ogni giorno = every day
• ogni settimana = every week
• ogni anno = every year

This works much like English. You would not say every the day, and Italian likewise does not say ogni il giorno.

It is most naturally understood in a general sense: if you change the water every day, meaning if someone does that or if one does that.

Italian often uses the tu form this way, especially in everyday speech, instructions, and advice. So it does not necessarily mean the florist is talking to one specific person in a very personal way.

A more impersonal version could be:

• ...se si cambia l’acqua ogni giorno

But se cambi l’acqua ogni giorno sounds very natural and conversational.