La sigaretta è vicino al tavolo.

La is the feminine singular definite article, meaning the.

• sigaretta is a feminine singular noun
• so it takes la
• la sigaretta = the cigarette

In Italian, articles are used very often, sometimes more often than in English.

È with an accent is the verb is, from essere (to be).

• è = is
• e without an accent = and

So:

• La sigaretta è vicino al tavolo = The cigarette is near the table
• La sigaretta e il tavolo would mean The cigarette and the table

The accent is important because it changes the meaning completely.

Here vicino means near or close.

It is used with a when followed by a noun:

• vicino a = near / close to

In the sentence, a combines with il to make al:

• vicino al tavolo = near the table

Because in Italian, a + il contracts to al.

This is very common:

• a + il = al
• a + lo = allo
• a + la = alla
• a + i = ai
• a + gli = agli
• a + le = alle

So:

• vicino a il tavolo is not correct
• vicino al tavolo is correct

This is a very good question, and many learners notice it.

In standard Italian, many speakers would prefer:

• La sigaretta è vicina al tavolo

because vicina agrees with la sigaretta, which is feminine singular.

Why, then, might you see vicino?

• vicino can sometimes be felt as more fixed or adverb-like in certain uses
• but with essere, agreement is usually expected by many speakers

So for a learner, the safest and most standard version is:

• La sigaretta è vicina al tavolo

If your textbook or exercise gives vicino, it may be simplifying the structure, but vicina is usually the better choice here.

It can behave like both, depending on the context.

As an adjective, it agrees with the noun:

• il tavolo è vicino
• la sedia è vicina
• i libri sono vicini
• le chiavi sono vicine

As an adverb, it stays unchanged and means nearby:

• Abito vicino = I live nearby

In your sentence, because it describes where la sigaretta is, learners are usually taught to treat it like an adjective, so agreement is common:

• La sigaretta è vicina al tavolo

Italian does use a preposition here: a.

English says:

• near the table

Italian says:

• vicino a/al tavolo

So the structure is slightly different. Italian normally wants a after vicino when a noun follows.

Examples:

• vicino alla porta = near the door
• vicino al muro = near the wall

Yes, Italian word order is somewhat flexible, though the basic order here is very normal:

• La sigaretta è vicina al tavolo

You could also say:

• Vicino al tavolo c'è la sigaretta = Near the table there is the cigarette

That version changes the focus a bit. It sounds more like you are introducing the location first.

But for a simple neutral sentence, La sigaretta è vicina al tavolo is the clearest pattern.

Yes. Grammatically, that is fine:

• Il tavolo è vicino alla sigaretta = The table is near the cigarette

It describes the same spatial relationship, just from the other object's point of view.

Notice the contraction:

• a + la = alla
• so vicino alla sigaretta

Yes, depending on the exact meaning.

Common alternatives are:

• accanto a = next to / beside
• presso = near / by in some contexts, often more formal
• nei pressi di = in the vicinity of, more formal

Examples:

• La sigaretta è accanto al tavolo = The cigarette is next to the table
• La sigaretta è vicina al tavolo = The cigarette is near the table

Accanto a usually sounds more specifically beside/right next to, while vicino a can be a bit broader.

A simple pronunciation guide:

• sigaretta ≈ see-ga-RET-ta
• vicino ≈ vee-CHEE-no

A couple of useful points:

• in ci, the c sounds like ch before i or e
• the stress in sigaretta falls on ret
• the stress in vicino falls on ci

So:

• si-ga-RET-ta
• vi-CI-no

Yes. It has everything needed for a complete sentence:

• La sigaretta = the subject
• è = the verb
• vicino/vicina al tavolo = the description of location

So structurally it is complete.

That said, the most standard version would usually be:

• La sigaretta è vicina al tavolo

because of agreement with the feminine noun sigaretta.