Teorik eğitimden sonra uygulamalı eğitim başlıyor.

Literally, it is:

• teorik eğitim = theoretical training / theoretical education
• -den = from
• sonra = after

So teorik eğitimden sonra literally means after the theoretical training.

In natural English, you would usually translate the whole sentence as After the theoretical training, the practical training begins or Practical training starts after the theoretical training.

Because sonra normally requires the noun before it to be in the ablative case.

The ablative ending is:

• -dan / -den / -tan / -ten

Here:

• eğitim
  • -den → eğitimden

So:

• eğitimden sonra = after the training

A very common pattern in Turkish is:

• dersten sonra = after class
• işten sonra = after work
• yemekten sonra = after the meal / after eating

Because Turkish uses many postpositions where English uses prepositions.

English says:

• after the theoretical training

Turkish says:

• theoretical training-from after
• teorik eğitimden sonra

So sonra works like after, but it comes after the noun phrase, not before it.

Uygulamalı means practical, applied, or with practice/application depending on context.

In uygulamalı eğitim, it means practical training.

It comes from:

• uygulama = application, practice
• -lı / -li / -lu / -lü = with, having

So uygulamalı is basically with practice/application, which is why it becomes practical or applied in English.

No. They only look similar.

In this sentence, uygulamalı is not the necessity ending.

Here the word is:

• uygulama
  • -lı → uygulamalı

That -lı is an adjective-forming suffix meaning something like with or having.

By contrast, the necessity suffix is attached to a verb, for example:

• gitmeli = he/she should go
• yapmalıyım = I must do it

So uygulamalı eğitim does not mean training that must be applied. It means practical/applied training.

Turkish usually does not use articles like the or a/an the way English does.

So:

• teorik eğitim can mean theoretical training
• uygulamalı eğitim can mean practical training

Whether English needs the depends on context. In this sentence, English naturally uses the because we are talking about specific stages in a program:

• After the theoretical training, the practical training begins.

But Turkish does not need separate words for that.

Yes, -yor is the Turkish present continuous marker, and literally başlıyor is is starting / is beginning.

But in Turkish, this form is also often used for:

• current actions
• near-future actions
• scheduled or regular events

So in this sentence, başlıyor can naturally be translated as:

• starts
• begins
• is starting

Depending on context, English may prefer the simple present even though Turkish uses -yor.

The dictionary form is başlamak, meaning to start / to begin.

It is built like this:

• başla- = verb stem
• -ıyor / -iyor / -uyor / -üyor = present continuous suffix

So:

• başla-yor → başlıyor

The vowel changes according to vowel harmony, and spelling adjusts accordingly.

So başlıyor means is starting / starts.

No, Turkish word order is flexible, although some orders sound more natural in neutral speech.

This sentence:

• Teorik eğitimden sonra uygulamalı eğitim başlıyor.

puts the time sequence first: After the theoretical training...

You could also say:

• Uygulamalı eğitim teorik eğitimden sonra başlıyor.

That still means the same thing, but the emphasis shifts slightly toward uygulamalı eğitim.

A very common neutral pattern in Turkish is:

• [time/context] + [subject] + [verb]

and that is exactly what this sentence does.

Because in Turkish, adjectives normally come before the noun they describe, just like in English.

So:

• teorik eğitim = theoretical training
• uygulamalı eğitim = practical training

Also, Turkish adjectives do not change form for singular/plural or gender.

So the adjective stays the same:

• teorik eğitim
• teorik ders
• teorik bilgiler

No agreement changes are needed.

It could, depending on context, but in a sentence like this it more often describes a sequence or program structure:

• first theoretical training
• then practical training

So the most natural interpretation is something like:

• Practical training begins after theoretical training
• After the theoretical part, the practical part starts

If someone were describing a live event happening at this moment, başlıyor could also mean is starting now, but the sentence by itself does not force that reading.

A few letters here are especially important for English speakers:

• ğ in eğitim: this letter usually is not pronounced like a hard g in modern Turkish. It often lengthens or smooths the surrounding vowel sound. So eğitim sounds roughly like eh-i-tim with a glide, not egg-itim.
• ş in başlıyor: pronounced like sh in ship
• ı in başlıyor: this is the dotless i, a sound English does not really have. It is a central vowel, somewhat like a relaxed vowel in unstressed syllables, but you should not pronounce it like ee.
• ö and ü are not in this sentence, but they are also common Turkish vowel sounds English speakers need to learn carefully.

A rough learner-friendly pronunciation might be:

• teorik ≈ teh-oh-rik
• eğitimden ≈ eh-ee-tim-den
• sonra ≈ son-rah
• uygulamalı ≈ oo-ygoo-lah-ma-luh
• başlıyor ≈ bash-luh-yor

These are only approximations, but they can help at first.