La afabla kelnerino ridetas al ĉiuj gastoj.

La is the definite article in Esperanto, like the in English.

A few useful things about la:

• It does not change for singular or plural.
• It does not change for gender.
• It usually does not change for case either.

So:

• la kelnerino = the waitress
• la gastoj = the guests

In this sentence, la afabla kelnerino means a specific, identifiable waitress: the kind waitress.

Words ending in -a are adjectives in Esperanto.

So afabla is an adjective describing kelnerino.

• afabla = kind, friendly
• kelnerino = waitress

Together:

• afabla kelnerino = kind waitress
• la afabla kelnerino = the kind waitress

The -a ending is the normal adjective ending in Esperanto.

The core word is kelnero, meaning waiter or sometimes server.
The suffix -in- adds a female meaning.

So:

• kelnero = waiter / server
• kelnerino = waitress

Breakdown:

• kelner- = the root
• -in- = female
• -o = noun ending

So kelnerino literally means female server.

Ridetas can be broken into parts:

• rid- = the idea of laughing
• -et- = a small or slight version of something
• -as = present tense

So:

• ridas = laughs
• ridetas = smiles, or laughs lightly

This is a very common Esperanto word-building pattern.
The suffix -et- often gives a weaker, smaller, or gentler version of the base meaning.

Because Esperanto often builds new meanings very logically from roots and affixes.

The verb ridi means to laugh.
Adding -et- gives the idea of laughing a little or lightly laughing, which becomes smiling:

• ridi = to laugh
• rideti = to smile

So even if it may feel unusual at first to an English speaker, it is very natural in Esperanto.

Because in Esperanto, rideti al iu means to smile at someone.

So:

• ridetas al la gastoj = smiles at the guests

The preposition al usually means to or toward, but with some verbs it corresponds to English at.

This is just the normal pattern for this verb:

• paroli al iu = speak to someone
• skribi al iu = write to someone
• rideti al iu = smile at someone

Because gastoj is part of the prepositional phrase al ĉiuj gastoj.

After a preposition like al, nouns normally do not take the accusative -n.

So:

• al ĉiuj gastoj = to/at all the guests

If you wrote gastojn, that would be wrong here.

A helpful rule for beginners:

• direct object often gets -n
• noun after a preposition usually does not

In this sentence, the guests are not a direct object. They are the people the waitress is smiling at.

Because gastoj is plural, and ĉiuj agrees with it.

Compare:

• ĉiu gasto = each guest / every guest
• ĉiuj gastoj = all guests

In this sentence, the meaning is all the guests, so Esperanto uses the plural form ĉiuj.

That -j is the plural marker.

In Esperanto, plural is marked with -j.

Here is the pattern in the sentence:

• kelnerino = singular, so no -j
• afabla describes kelnerino, so it also stays singular
• gastoj = plural, so it takes -j
• ĉiuj describes gastoj, so it also takes -j

So the matching is:

• la afabla kelnerino = singular
• ĉiuj gastoj = plural

Adjectives and similar describing words agree with the noun in number.

Yes. Esperanto word order is more flexible than English word order.

The neutral, most straightforward order here is:

• La afabla kelnerino ridetas al ĉiuj gastoj.

But other orders are possible, especially for emphasis, for example:

• Al ĉiuj gastoj ridetas la afabla kelnerino.

That might emphasize all the guests.

Even so, the original version is the most natural one for a learner to use.

A rough pronunciation guide:

• ĉ sounds like ch in church
• j sounds like English y in yes

So ĉiuj is approximately:

• CHEE-ooy

More carefully, it is something like:

• ĉi-uj

Also:

• g in gastoj is always a hard g, like in go
• j in gastoj sounds like y, so gastoj is roughly GAH-stoy

It can often mean either kind or friendly, depending on context.

The basic idea is that the person is pleasant, nice, or gracious.
So in different situations, afabla may be translated as:

• kind
• friendly
• polite
• courteous

In this sentence, kind or friendly would both fit well.

The sentence follows a very clear pattern:

• La afabla kelnerino = subject
• ridetas = verb
• al ĉiuj gastoj = prepositional phrase

So structurally it is:

• [subject] [verb] [prepositional phrase]

That is one of the most common and easiest Esperanto sentence patterns.