La dentisto klarigis kiel uzi buŝakvon kaj kontraŭdolorilon.

In Esperanto, -is marks the past tense. So klarigis means explained.

• klarigi = to explain
• klarigas = explains / is explaining
• klarigis = explained
• klarigos = will explain

So La dentisto klarigis... means The dentist explained...

Because after klarigis (explained), Esperanto normally uses the infinitive to express how to do something.

• kiel uzi = how to use
• uzi is the infinitive: to use

So the structure is very similar to English:

• The dentist explained how to use...
• La dentisto klarigis kiel uzi...

Using uzu would be an imperative/jussive idea, more like use! or let someone use, which is not what is meant here.

The -n ending marks the direct object in Esperanto.

Here, both things are the objects of uzi (to use):

• use mouthwash
• use a painkiller

So:

• buŝakvo → buŝakvon
• kontraŭdolorilo → kontraŭdolorilon

They are both singular direct objects linked by kaj (and).

Esperanto has the definite article la, but it does not have a separate indefinite article like English a/an.

So:

• la dentisto = the dentist
• buŝakvon can mean mouthwash or a mouthwash, depending on context
• kontraŭdolorilon can mean a painkiller or just painkiller in a general sense

In other words, Esperanto often leaves the indefinite idea unmarked.

Yes. -isto is a very useful Esperanto suffix. It usually means a person professionally associated with something or someone who practices something.

So:

• dento = tooth
• dentisto = dentist

Other examples:

• piano → pianisto = pianist
• arto → artisto = artist
• scienco → sciencisto = scientist

So recognizing -isto helps you guess many job and profession words.

Yes, it is a compound word.

• buŝo = mouth
• akvo = water

Together, buŝakvo literally means mouth-water, that is, mouthwash.

In Esperanto compounds, the final part is usually the main idea, and the earlier part modifies it. So buŝakvo is a kind of akvo related to the buŝo.

It is also a compound/derived word:

• kontraŭ = against
• doloro = pain
• -ilo = tool, instrument, or means for doing something

So kontraŭdolorilo literally means something like a thing used against pain. In normal English, that is painkiller or pain-relief medicine.

This is a very Esperanto-like way of building vocabulary from smaller meaningful parts.

Yes. kaj means and, and here it links two direct objects of uzi:

• uzi buŝakvon
• uzi kontraŭdolorilon

So the sentence means that the dentist explained how to use both of those things.

Yes. That is the natural reading.

The phrase means how to use mouthwash and a painkiller. Since both nouns are objects of the same verb uzi, the instruction applies to both.

If needed, Esperanto could make the repetition more explicit, but in this sentence the shared verb is completely normal and clear.

The basic order is:

• La dentisto = subject
• klarigis = verb
• kiel uzi buŝakvon kaj kontraŭdolorilon = what was explained

So it is essentially:

[Subject] [Verb] [Content]

Esperanto often uses a fairly English-like word order, even though its endings allow more flexibility.

The two letters that often catch English speakers are:

• ŝ = sh sound, like in shoe
• ŭ = a short w-like glide, often heard in diphthongs such as aŭ

So:

• buŝakvon has ŝ = sh
• kontraŭdolorilon has aŭ, which sounds roughly like the ow in cow

Also remember that Esperanto spelling is very regular: each letter has one consistent sound.

kiel is not a noun or adjective. It is a correlative/adverb-like question-and-relationship word meaning how.

So:

• kiel = how
• uzi = to use

Together: kiel uzi = how to use

Because kiel is not a noun, adjective, or direct object, it does not take endings like -o, -a, or -n.