Adam yüksek sesle bağırdı.

Adam can mean the man or simply man/a man, depending on context. Turkish often leaves definiteness less explicit than English.

• Adam bağırdı. = The man shouted / A man shouted
• Bir adam bağırdı. = A man shouted (more clearly introducing a new, unknown man)

So if the sentence is presented by itself, adam is perfectly natural.

It literally means with a high/loud voice.

Breakdown:

• yüksek = high, loud
• ses = voice, sound
• -le = with, by means of

So yüksek sesle bağırdı is literally something like shouted with a loud voice, which is how Turkish commonly expresses loudly.

The ending -le / -la is an instrumental/comitative suffix meaning with.

• ses = voice
• sesle = with a voice / in a voice

Because of vowel harmony, the suffix appears as -le here, not -la.

This suffix is very common in adverb-like expressions:

• yavaşça = slowly
• dikkatle = carefully
• sessizce = quietly
• yüksek sesle = loudly

Turkish often uses noun phrases where English uses adverbs.

So instead of one adverb meaning exactly loudly, Turkish very naturally says:

• yüksek sesle = in a loud voice / loudly

This is one of the most common ways to say it. It is idiomatic and very normal.

It describes ses.

So the structure is:

• yüksek sesle = with a loud voice

Not:

• yüksek adam = a tall/high man or something similar

In the sentence, yüksek belongs to sesle, forming a unit that describes how the shouting happened.

Bağırdı is in the simple past tense.

Breakdown:

• bağır- = shout
• -dı = past tense

So:

• bağırdı = he/she/it shouted

Since the subject is adam, the full sentence means the man shouted.

The past tense suffix in Turkish changes form according to vowel harmony and consonant voicing:

• -dı, -di, -du, -dü
• -tı, -ti, -tu, -tü

In bağırdı:

• the last vowel of bağır- is ı, so the suffix uses the ı form
• the stem ends in r, which is voiced, so the suffix begins with d, not t

That gives -dı.

Turkish usually does not need subject pronouns when the subject is already clear.

Here, the subject is explicitly stated as adam, so there is no need for o.

• Adam bağırdı. = The man shouted.
• O bağırdı. = He/She shouted.

Turkish often avoids unnecessary pronouns more than English does.

Turkish normally prefers Subject + Other elements + Verb word order.

So:

• Adam = subject
• yüksek sesle = manner expression
• bağırdı = verb

This makes the sentence very standard and neutral.

English usually puts the verb earlier:

• The man shouted loudly.

Turkish often saves the main verb for the end.

Yes, Turkish word order is flexible, but different orders change emphasis.

Neutral order:

• Adam yüksek sesle bağırdı.

Other possible orders:

• Yüksek sesle adam bağırdı. = emphasizes loudly
• Adam bağırdı yüksek sesle. = possible in speech, often more marked

The version you were given is the most natural basic order for learners.

Here it is intransitive, so it does not take a direct object.

• bağırmak = to shout

That is why there is no accusative-marked object in the sentence.
The man is simply performing the action of shouting.

In modern Turkish, ğ usually is not pronounced as a strong consonant like English g.

In bağırdı, it mainly lengthens or smooths the preceding vowel:

• bağırdı sounds approximately like baa-ır-dı or baırdı, depending on accent and speed

So do not pronounce it like a hard g.

Also note:

• ı is the Turkish vowel with no exact English equivalent
• dı sounds roughly like duh without a strong u

Yes, you can.

• yüksek sesle = loudly / in a loud voice
• yüksek bir sesle = with a loud voice

The version without bir is shorter and very common.
The version with bir can sound a little more descriptive or explicit.

So both are correct, but yüksek sesle bağırdı is the more straightforward everyday phrasing.

The dictionary form is bağırmak, which means to shout.

To get from dictionary form to the sentence form:

• remove -mak
• add the appropriate tense suffix

So:

• bağırmak → bağırdı

This is a useful pattern to remember for many Turkish verbs.