Je ne bois presque jamais de café le soir.

Because the verb is boire (to drink), and with je in the present tense it becomes bois.

Present tense of boire:

• je bois
• tu bois
• il/elle/on boit
• nous buvons
• vous buvez
• ils/elles boivent

So je bois means I drink.

In standard French, negation is usually made with two parts:

• ne before the verb
• another negative word after the verb, such as pas, jamais, plus, rien, etc.

Here:

• ne ... jamais = never
• presque jamais = almost never

So in Je ne bois presque jamais..., the ne is part of the normal negative structure.

In everyday spoken French, people often drop ne:

• Je bois presque jamais de café le soir.

But in careful speech and writing, ne is expected.

Because jamais alone means never, while presque jamais means almost never.

Compare:

• Je ne bois jamais de café le soir. = I never drink coffee in the evening.
• Je ne bois presque jamais de café le soir. = I almost never drink coffee in the evening.

So presque softens jamais.

After negation, French usually changes du / de la / de l' / des to de.

Positive:

• Je bois du café le soir. = I drink coffee in the evening.

Negative:

• Je ne bois pas de café le soir.
• Je ne bois jamais de café le soir.
• Je ne bois presque jamais de café le soir.

So de café is the normal form after a negative structure.

A common exception is with être:

• C'est du café.
• Ce n'est pas du café.

But with boire, after negation, de café is correct.

It comes after the conjugated verb:

• Je ne bois presque jamais...

A useful pattern is:

subject + ne + verb + presque jamais + noun/complement

Examples:

• Je ne mange presque jamais de viande.
• Il ne sort presque jamais.
• Nous ne regardons presque jamais la télé.

So you do not put presque jamais before bois here.

Le soir means in the evening or at night, depending on context.

In French, expressions like these often use the definite article:

• le matin = in the morning
• l'après-midi = in the afternoon
• le soir = in the evening

So French says literally something like the evening, where English usually says in the evening.

Because French often uses time expressions without a preposition where English uses one.

So:

• le matin = in the morning
• le soir = in the evening

You just learn these as fixed time expressions.
French does not need dans here.

Yes, but it is not exactly the same.

• Je ne bois presque jamais de café le soir = I almost never drink coffee in the evening.
• Je ne bois pas souvent de café le soir = I do not often drink coffee in the evening.

The second one is less strong.
Presque jamais suggests something very rare.
Pas souvent just means not often.

Usually, yes, in modern beginner-level French it is most often used in a negative structure:

• Je ne bois jamais de café.

But in some contexts, especially formal or literary French, jamais can mean ever:

• As-tu jamais vu ça ? = Have you ever seen that?

For this sentence, though, you should understand jamais as part of negation: never.

In everyday speech, many speakers drop ne:

• Je bois presque jamais de café le soir.

That is very common in conversation.

Also, pronunciation tends to flow together:

• Je often sounds like j' or chə
• ne may disappear completely in speech

But for writing, classwork, and careful French, keep:

• Je ne bois presque jamais de café le soir.

Bois is pronounced roughly like bwa.

So:

• je bois sounds approximately like zhuh bwa

A few pronunciation notes:

• j in je sounds like the s in measure
• oi in bois sounds like wa
• the final s in bois is silent

Yes, in a way. After negation, de + noun often has a general sense, like any or just an unspecified amount.

So:

• Je ne bois presque jamais de café means I almost never drink coffee / any coffee.

It does not refer to a specific coffee. It means coffee in general.

Because the French present tense is used for both:

• what is happening now
• general habits
• repeated actions

So Je ne bois presque jamais de café le soir means a general habit:

• I almost never drink coffee in the evening.

This is normal in both French and English.

Some parts can move, but the original order is the most natural.

Standard and natural:

• Je ne bois presque jamais de café le soir.

You could also say:

• Le soir, je ne bois presque jamais de café.

That puts more emphasis on in the evening.

But you would not normally say:

• Je presque jamais ne bois...
  or
• Je ne presque jamais bois...

So keep ne + verb + presque jamais together.

It breaks down like this:

• Je = subject
• ne ... presque jamais = negative adverb structure meaning almost never
• bois = verb
• de café = object
• le soir = time expression

So the pattern is:

subject + ne + verb + presque jamais + de + noun + time expression

That pattern is very useful for making similar sentences:

• Je ne mange presque jamais de viande le midi.
• Il ne regarde presque jamais la télé le soir.
• Nous ne buvons presque jamais de soda.