Nějaký fanoušek už tleská.

Here nějaký means some or a certain:

• Nějaký fanoušek = some fan / a certain fan

It often introduces a person or thing that is not specifically identified.

Depending on context, nějaký can also mean things like:

• some kind of
• any (in some questions or negative contexts)
• sometimes even a slightly dismissive some ... or other

But in this sentence, the most natural reading is simply some fan.

Because fanoušek is the subject of the sentence, so it is in the nominative singular.

• fanoušek = nominative singular, a fan
• fanouška would usually be genitive singular or accusative singular for a masculine animate noun

Since the sentence means Some fan is already clapping, the fan is the one doing the action, so nominative is required.

Nějaký has to agree with fanoušek in:

• gender: masculine
• number: singular
• case: nominative

So the masculine singular nominative form is nějaký.

This is normal adjective-type agreement in Czech. Even though nějaký is often translated as some, grammatically it behaves like an adjective.

Už usually means already.

So:

• už tleská = is already clapping

It suggests that the action has started, or that it is happening earlier than expected, or now at this point.

In some contexts, už can also feel like now or by now, but already is the clearest translation here.

Tleská is the 3rd person singular present tense of tleskat.

So it means:

• he/she/it claps
• or more naturally in context: is clapping / is applauding

Because the subject is nějaký fanoušek (some fan), the verb is in singular:

• fanoušek tleská = the fan is clapping

Because Czech has no articles like English a/an/the.

So a bare noun like fanoušek can mean:

• a fan
• the fan
• sometimes just fan in a general sense

The context tells you which one is meant.

In this sentence, nějaký helps make the noun clearly indefinite, so nějaký fanoušek naturally corresponds to some fan or a certain fan.

In Czech present tense, both are often possible depending on context.

So tleská can mean:

• claps
• is clapping
• is applauding

In this sentence, because of už and the situation it suggests, English often sounds more natural with the progressive:

• Some fan is already clapping.

But Some fan already claps would sound less natural in English unless you meant a habitual action.

Czech usually does not need subject pronouns when the verb form already shows the person and number.

So instead of saying:

• On tleská

Czech can simply say:

• Tleská

Here the noun nějaký fanoušek is already present, so adding on would be unnecessary.

Yes. Czech word order is fairly flexible, and changing it changes the focus or emphasis, not usually the basic meaning.

For example:

• Nějaký fanoušek už tleská.
  Neutral: Some fan is already clapping.

• Už tleská nějaký fanoušek.
  More like: Some fan is already clapping / There’s already a fan clapping.

• Tleská už nějaký fanoušek.
  This can sound more marked, often depending on what is being emphasized.

The given sentence is a very natural neutral order.

Yes. Fanoušek is masculine animate.

That matters because masculine animate nouns have special case patterns, especially in the singular and plural.

For example:

• nominative singular: fanoušek
• accusative singular: fanouška

This is one reason learners often ask why the form changes in other sentences.

This is a useful aspect question.

• tleskat = to clap / be clapping / clap repeatedly
  imperfective
• zatleskat = to clap once / start clapping / give applause
  perfective

So:

• Nějaký fanoušek už tleská. = Some fan is already clapping.
• Nějaký fanoušek už zatleskal. = Some fan has already clapped / gave a clap / started the applause

In your sentence, tleská focuses on the action as ongoing.

A rough guide for an English speaker:

• Nějaký ≈ NYEH-yah-kee
• fanoušek ≈ FAH-noh-shek
• už ≈ oozh
• tleská ≈ TLYES-kaa

A few helpful notes:

• ě often causes a ny / ty / dy-type pronunciation before certain consonants; in ně, it sounds like nye
• š sounds like sh
• ž sounds like the s in measure
• á is a long vowel

The stress in Czech is normally on the first syllable of each word:

• NĚjaký
• FAnoušek
• Už
• TLEská