Eve gelince pijamamı giydim ve terliklerimi kapının yanına bıraktım.

Turkish often drops subject pronouns when they are already clear from the verb ending.

Here, giydim means I wore/put on and bıraktım means I left. The -m ending shows first person singular, so ben is unnecessary.

So this is completely natural Turkish:

• Pijamamı giydim = I put on my pajamas
• Ben pijamamı giydim = also possible, but more emphatic

Because eve shows movement toward home.

• ev = house, home
• ev-e = to home / homeward
• ev-de = at home / in the house

So:

• eve gelmek = to come home
• evde olmak = to be at home

In this sentence, the person is arriving home, so eve is the correct form.

Gelince is a converb form meaning when (someone) comes/came or upon coming.

It is formed from:

• gel- = come
• -ince / -ınca = when, once, upon

So:

• gelince = when [someone] came/came home in this context

In Eve gelince, it means when I came home.

This structure is very common in Turkish:

• seni görünce = when I saw you
• bitirince = when/after finishing
• eve varınca = when I arrived home

The form gelince itself does not show person. The subject is understood from context, and usually it is the same subject as the main clause unless something else is stated.

Since the main verbs are:

• giydim = I put on
• bıraktım = I left

the sentence is naturally understood as:

• When I came home, I put on my pajamas and left my slippers by the door.

If the subject were different, Turkish would usually make that clear:

• Ali eve gelince pijamalarını giydi. = When Ali came home, he put on his pajamas.

Pijamamı contains both a possessive ending and an accusative ending.

Breakdown:

• pijama = pajamas / pajama set
• pijama-m = my pajamas
• pijama-m-ı = my pajamas as a definite direct object

So:

• pijamamı giydim = I put on my pajamas

The final -ı is there because the object is specific and definite.

Turkish often uses pijama as a singular noun meaning a pajama set or sleepwear, even where English prefers the plural pajamas.

So:

• pijamamı giydim sounds very natural in Turkish

You may also hear plural forms in some contexts, but singular pijama is very common for the general item of clothing.

This is one of those places where Turkish and English organize vocabulary differently.

Because giydim means I put on / wore a specific item of clothing, while giyindim means more generally I got dressed.

• pijamamı giydim = I put on my pajamas
• giyindim = I got dressed

So if you mention the clothing item directly, giymek is the normal choice:

• montumu giydim = I put on my coat
• ayakkabılarımı giydim = I put on my shoes

Yes:

• terlik = slipper
• terlikler = slippers
• terliklerim = my slippers
• terliklerimi = my slippers as a definite direct object

So the full breakdown is:

• terlik-ler-im-i

This means:

• -ler = plural
• -im = my
• -i = accusative

In English, slippers is naturally plural, and Turkish also commonly uses the plural here.

Because both are definite direct objects.

In this sentence, the speaker is referring to:

• my pajamas
• my slippers

These are specific, known items, not indefinite ones. Turkish usually marks such direct objects with the accusative.

Compare:

• Pijama giydim. = I wore pajamas / I put on some pajamas
• Pijamamı giydim. = I put on my pajamas

And:

• Terlik aldım. = I bought slippers / some slippers
• Terliklerimi bıraktım. = I left my slippers

This is a very common Turkish structure.

Breakdown:

• kapı = door
• kapı-nın = of the door
• yan = side
• yan-ı = its side / the side of it
• yan-ı-na = to its side

So:

• kapının yanına literally means to the side of the door
• natural English: next to the door / by the door

Turkish often uses these location nouns in the same way:

• üst = top
• alt = bottom / underneath
• ön = front
• arka = back
• yan = side

Examples:

• masanın üstüne = onto the table / on top of the table
• evin önüne = to the front of the house
• kapının yanına = next to the door

Yanına uses the dative and suggests movement or placement to that spot.

• yanına = to next to / to the side of
• yanında = at next to / beside

With bırakmak, both can appear, but the nuance is a little different:

• kapının yanına bıraktım = I placed/left them next to the door
• kapının yanında bıraktım = I left them at the side of the door / they were left there

In your sentence, yanına highlights the destination of the action: the slippers were put to that place.

Both can work, but they are not exactly the same.

• koymak = to put, place
• bırakmak = to leave, put down, leave behind

So:

• terliklerimi kapının yanına koydum = I put my slippers next to the door
• terliklerimi kapının yanına bıraktım = I left my slippers next to the door

In this sentence, bıraktım slightly emphasizes that the slippers were left there after being taken off.

Both are the simple past tense, but the suffix changes form because of normal Turkish sound rules.

The past tense is basically -DI, but it changes according to:

• vowel harmony
• consonant voicing

So:

• giy-di-m = I wore / I put on
• bırak-tı-m = I left

Why -tı after bırak-? Because the verb stem ends in the voiceless consonant k, so the past suffix becomes t instead of d.

This is the same pattern as:

• git-ti-m = I went
• bak-tı-m = I looked
• bul-du-m = I found
• sev-di-m = I loved

Because Turkish normally prefers Subject-Object-Verb order, and the verb often comes last.

In your sentence:

• pijamamı giydim
• terliklerimi kapının yanına bıraktım

This is very typical Turkish structure.

Also, Eve gelince is placed first because it sets the time frame:

• When I came home, ...

So the sentence flows like this:

1. time/background
2. object(s)
3. verb(s)

That is much more natural in Turkish than copying English word order.