If you want to stay in Turkey beyond the visa-free window, you need an ikamet izni, a residence permit. The process runs through the Göç İdaresi, the migration authority, and it is well organised but mercilessly formal. A missing piece of paper does not produce a follow-up question. It produces a new appointment.
Two things catch newcomers out with some regularity. First, the appointment is booked online and the system assigns it to you; you do not simply pick a convenient morning, and if the date it gives you is inconvenient, that is now your problem rather than the system's. Second, your rental contract is not acceptable in the state you signed it in. It has to be certified by the noter, the notary, which costs both time and money that almost nobody budgets for.
The words below are not a language course. They are what gets said in that building, on the phone about that building, and printed on the paperwork you carry into it.
On pronunciation: Turkish is written almost exactly as it sounds, which makes the entry easier than it looks. c is the "j" in "jam". ç is "ch". ş is "sh". ğ is silent and simply stretches the vowel in front of it. The dotless ı is a dull vowel with no English equivalent, closest to the "a" in "about". Two letters will be genuinely unfamiliar: ö is roughly the vowel in "bird" but with your lips rounded, and ü is the "ee" of "see" said with your lips pushed forward into a whistle. In the transliterations below they appear as "ur" and "ew", which is an approximation and nothing more.
The office and getting through the door
Göç İdaresi (gurch ee-dah-re-see): the migration authority. The full official name is much longer, but this is what everyone calls it.
Randevu (rahn-de-voo): the appointment. Borrowed from French, and easy to remember once you spot the rendez-vous inside it.
e-Devlet (eh-dev-let): the state online portal. Practically every administrative process begins here, and without access to it you are remarkably helpless in Turkey.
Nüfus Müdürlüğü (new-fooss mew-dewr-lew-ew): the civil registry office, responsible for address records and ID documents.
Sıra numarası (suh-ruh noo-ma-ra-suh): the queue number.
Görevli (gur-ev-lee): the official, the person on duty at the counter.
Your documents
Pasaport (pa-sa-port): the passport.
Yabancı kimlik numarası (ya-ban-juh kim-leek noo-ma-ra-suh): the foreigner identification number, shortened to YKN. It always begins with 99, and from the moment you have one it becomes the most important number in your life in Turkey.
İkametgah (ee-ka-met-gah): the place of residence, and in an official context the residence certificate as well.
Kira sözleşmesi (kee-ra surz-lesh-me-see): the rental contract. For the application you need it as a noter tasdikli kira sözleşmesi, meaning notarised.
Noter (no-tehr): the notary. A central figure in Turkish daily life, and far more present than you are likely to be used to.
Yeminli tercüman (ye-min-lee ter-jew-mahn): the sworn translator. Documents from your home country will as a rule need a certified translation.
Apostil (a-pos-teel): the apostille. Get it in your home country before you fly. Arranging one after the fact is a genuine ordeal.
Sağlık sigortası (sah-luhk see-gor-ta-suh): health insurance. Proof of cover is a precondition for the permit.
Biyometrik fotoğraf (bee-yo-met-reek fo-to-raf): the biometric passport photo. Bring more than they ask for.
The procedures
Başvuru (bash-voo-roo): the application. Both the act of applying and the file that results from it.
İkamet izni (ee-ka-met eez-nee): the residence permit. Colloquially a lot of people just say oturma izni (o-toor-ma eez-nee), literally "sitting permission".
Uzatma (oo-zat-ma): the extension.
Harç (harch): the fee.
Belge (bel-ge): the document. Evrak (ev-rak) means the whole stack of them.
Fotokopi (fo-to-ko-pee): the photocopy. Same rule as everywhere else: more than you think.
İmza (eem-zah): the signature.
Onay (o-nigh): the confirmation, the approval.
The words you hopefully won't need
Eksik evrak (ek-seek ev-rak): missing documents.
Reddedildi (red-de-deel-dee): rejected.
İtiraz (ee-tee-raz): the appeal.
Vize ihlali (vee-ze eeh-lah-lee): a visa violation.
Sınır dışı (suh-nuhr duh-shuh): deportation. Literally "outside the border".
Tekrar gelin (tek-rar ge-leen): "come again". The sentence nobody wants.
Why this beats a translation app
There is no shortage of Turkish courses, and nearly all of them open in a café. That is not wrong, but it does nothing to prepare you for the morning on which somebody decides whether you get to stay. This particular vocabulary is specialised, it comes back identically at every renewal, and it is in no course book anywhere.
A phone helps you read a form. It does not help when a sentence is said once, quickly, across a counter, and the person saying it has eleven more people behind you. What you need there is recognition, already loaded, so that the word for "missing" or "notarised" lands the first time and you know which of the two mornings you are having.
That is precisely what Vokabulo is built for. You capture the words your own life puts in front of you and learn them in the context where you will meet them again. Turkish taught straight from English, with over 100 languages available in every combination.
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