Эти духи напоминают мне лето, и моя жена пользуется ими только по праздникам.

Context tells you. In Russian, духи can mean either perfume or spirits/ghosts. In normal writing, stress is not marked, but the meanings are often distinguished by stress:

• духи́ = perfume
• ду́хи = spirits/ghosts

In this sentence, эти, моя жена, and especially пользуется ими make it clear that the meaning is perfume.

Because духи in the meaning of perfume is a plural-only noun in Russian. That means Russian treats it grammatically as plural, even when English would often translate it as singular perfume.

So:

• эти духи = literally these perfumes
• but in natural English it can mean this perfume or these perfumes, depending on context

That is why the rest of the sentence also uses plural agreement.

They agree with духи, which is grammatically plural.

• эти = these
• напоминают = they remind

So Эти духи напоминают... literally means These perfumes remind...

Even if English might say This perfume reminds me of summer, Russian still uses plural grammar because духи is plural.

Because напоминать takes the person being reminded in the dative case.

The pattern is:

что-то напоминает кому-то что-то

So here:

• эти духи = the thing that causes the reminder
• мне = the person affected, in dative
• лето = what it reminds me of

So Эти духи напоминают мне лето means These perfumes remind me of summer.

Here лето is the direct object of напоминают, so it is in the accusative case.

For neuter inanimate nouns like лето, the nominative and accusative forms are the same, so you still see лето.

A useful comparison:

• напоминает мне лето = reminds me of summer
• напоминает мне о лете = reminds me about summer

Both are possible in Russian, but they are slightly different in structure and nuance. In your sentence, the meaning is more like makes me think of summer, so лето without a preposition fits very well.

In this sentence, the pattern is:

что-то напоминает кому-то что-то

That means:

• the subject is the thing that triggers the association
• the person is in the dative
• the thing remembered is the direct object

So:

• Эти духи = subject
• мне = dative
• лето = direct object

A very literal breakdown is: These perfumes remind to me summer, but natural English is These perfumes remind me of summer.

Because пользоваться takes the instrumental case.

The pattern is:

пользоваться чем? = to use something

So the pronoun они becomes ими in the instrumental plural:

• nominative: они
• instrumental: ими

That is why:

• пользуется ими = uses them

Not их, because их is accusative/genitive, and пользоваться does not take accusative.

Because the dictionary form of the verb is пользоваться, which means to use.

The -ся here is just part of the verb as it is normally used. It does not literally mean use oneself. Many Russian verbs simply happen to be -ся verbs and have their own standard meaning and case pattern.

So you should learn it as:

• пользоваться = to use
• пользоваться чем? = to use something

По праздникам means on holidays, on festive occasions, or more naturally in this sentence, for special occasions.

Here по is used with the dative plural in a time expression:

• праздники = holidays
• по праздникам = on holidays / on festive occasions

This is a common Russian expression. With только, it means:

• только по праздникам = only on holidays / only for special occasions

Here it means uses in general, as a habitual action.

Russian present tense can describe:

• what is happening now
• what happens regularly or generally

In this sentence, только по праздникам clearly shows a repeated habit, so the meaning is:

My wife only uses them on holidays / for special occasions.

Because it is limiting that whole time phrase.

• только по праздникам = only on holidays

So the idea is that her wife’s use of the perfume is restricted to special occasions.

If только were moved, the emphasis could change. Russian word order is flexible, but here this is the most natural neutral placement.

It is mostly neutral and natural.

• Эти духи напоминают мне лето is a normal way to present the idea
• и моя жена пользуется ими только по праздникам is also a normal neutral continuation

Russian word order is flexible, so you could move elements for emphasis, for example:

• Мне эти духи напоминают лето = emphasizes me
• По праздникам моя жена пользуется ими = emphasizes on holidays

But the original sentence is a very standard, natural order for everyday Russian.