كلما سجل لاعب هدفا، شجعه الجمهور.

كلما means whenever, every time, or each time that. It introduces a repeated relationship between two actions:

كلما سجل لاعب هدفا، شجعه الجمهور
= Whenever a player scored a goal, the crowd cheered him
or, depending on context, Whenever a player scores a goal, the crowd cheers him

So كلما is a very common way to express repeated events.

After كلما, Arabic often uses the past tense to describe actions that happen repeatedly. This is normal in MSA.

So:

كلما سجل ... شجعه ...

literally looks like Whenever a player scored ..., the crowd cheered him, but it can also express a general pattern, which English often translates with the present:

Whenever a player scores a goal, the crowd cheers him.

In other words, the Arabic past here does not necessarily mean one single event in the past. It can describe something habitual or repeated.

A fully vowelled version is:

كُلَّما سَجَّلَ لاعِبٌ هَدَفًا، شَجَّعَهُ الجُمْهورُ.

A rough pronunciation is:

kullamā sajjala lāʿibun hadafan, shajjaʿahu al-jumhūru

Two useful things to notice:

سجل is read here as سَجَّلَ
شجعه is read here as شَجَّعَهُ

In normal Arabic writing, short vowels and shadda are usually omitted, so learners have to infer them from context.

Yes, لاعب is the subject.

Arabic often uses verb–subject–object order, especially in formal written language. So:

سجل لاعب هدفا
literally: scored a player a goal

but naturally in English: A player scored a goal

So even though لاعب comes after the verb, it is still the doer of the action.

Because it means a player, not the player.

لاعب without ال is indefinite and gives a general meaning: any player, a player in general.

If the sentence had اللاعب, it would mean the player, referring to a specific one.

So:

لاعب = a player
اللاعب = the player

هدفا is the direct object of سجل, so it is in the accusative case, which is usually marked with fatḥatan on an indefinite noun:

هَدَفًا

In ordinary spelling, this often appears with an extra written alif at the end, so you see:

هدفا

So the ending shows that the word means a goal as the object of the verb:

سجل لاعب هدفا
= A player scored a goal

The ـه means him.

So شجعه breaks down as:

شجّع = he encouraged / cheered
ـه = him

Together:

شجعه = cheered him or encouraged him

The pronoun refers back to لاعب, the player.

For the same reason as in the first clause: Arabic often prefers verb first in a verbal sentence.

So:

شجعه الجمهور
literally: cheered him the crowd

but naturally in English: the crowd cheered him

Here, الجمهور is the subject of شجعه, even though it comes after the verb.

Yes, الجمهور refers to many people, but grammatically it is a singular collective noun in Arabic.

So Arabic treats it as a singular noun:

الجمهورُ شجّعه
or in verb-first order
شجّعه الجمهورُ

That is why the verb is singular, not plural.

This is similar to English words like the crowd or the audience, which refer to many people but can behave as singular nouns.

Because Arabic often uses an attached object pronoun instead of repeating the noun.

Instead of saying something like:

شجع الجمهور اللاعب

the sentence says:

شجعه الجمهور

This is very natural Arabic. Once لاعب has already been mentioned, using ـه for him is smoother and less repetitive.