Learn Hardcore Turkish: Lütfen duyuruyu dikkatle okuyunuz, ardından formu doldurunuz. - Please read the announcement carefully, then fill in the form.

Those are the accusative case markers for definite direct objects. In Turkish, when the object is specific/definite, you add -(y)ı/-(y)i/-(y)u/-(y)ü (chosen by vowel harmony).

duyuruyu = the/that announcement (definite)
formu = the/that form (definite) If the object is not specific, you normally leave it unmarked (or use bir):
bir duyuru okuyun = read an announcement (any)
bir form doldurun = fill out a form (any) The y in duyuruyu is a buffer consonant because the noun ends in a vowel (see below).

What exactly does the ending -unuz in okuyunuz and doldurunuz do?

It’s the polite/official second-person plural imperative, used for instructions and when addressing people with the polite siz. It corresponds to the formal, sign-like style seen in notices.

oku + y + unuz → okuyunuz
doldur + unuz → doldurunuz The vowel in -unuz/-iniz/-ınız/-ünüz follows vowel harmony.

Why is there a y in okuyunuz and duyuruyu?

Turkish inserts a buffer y when a word ending in a vowel takes a suffix beginning with a vowel, to avoid a vowel-vowel clash:

oku + unuz → oku-y-unuz → okuyunuz
duyuru + u → duyuru-y-u → duyuruyu

Can I say okuyun and doldurun instead of okuyunuz/doldurunuz?

Yes. -un/-ün/-ın/-in is also a 2nd-plural imperative. In practice:

okuyunuz/doldurunuz = very formal, official, written instructions.
okuyun/doldurun = neutral/less formal; common in speech and everyday writing. Both can address one person politely (the siz form) or a group.

Is lütfen redundant if the verb already has -unuz? Where should I place it?

It’s not redundant. Lütfen softens the command regardless of the ending. Placement:

Common: Lütfen … -iniz/-unuz.
Also fine: … -iniz/-unuz, lütfen. or … lütfen. For an even softer request, use a question form: … okur musunuz? / … doldurur musunuz?

What does ardından literally mean, and how is it formed?

Literally “from its back/after it.” Morphology: ardı (its back/after) + buffer n + ablative -dan → ardından. In usage it means “after that / then,” referring back to the previous action.

Could I use sonra instead of ardından? Any nuance?

Yes. sonra is the most general “after/then.” ardından is a bit more formal/literary and common in written instructions. Both are fine here:

… okuyunuz, ardından/sonra formu doldurunuz.

Is ardından a conjunction like “then,” or something else? Why the comma?

It’s an adverb/postposition functioning as a sentence adverb (“after that”). The sentence has two imperative clauses; a comma separates them. You could also use a period: Okuyunuz. Ardından formu doldurunuz. Using ve (“and”) would not guarantee sequence, so ardından is better when order matters.

Why dikkatle and not dikkatlice or dikkatli bir şekilde?

All three mean “carefully,” with register differences:

dikkatle = “with attention” (from dikkat + ile), concise and formal; common in instructions.
dikkatlice = more colloquial/natural in speech.
dikkatli bir şekilde = perfectly correct but wordy; neutral/formal. Any of them would be understood here.

How is dikkatle formed?

From dikkat (attention) + ile (with). When ile attaches, it often appears as -le/-la, yielding the set expression dikkatle “with attention,” used adverbially.

Can I change the word order? Where can dikkatle go?

Yes, Turkish word order is flexible. Neutral placements keep adverbs and objects before the verb:

Lütfen duyuruyu dikkatle okuyunuz.
Lütfen dikkatle duyuruyu okuyunuz. Postverbal dikkatle (e.g., okuyunuz dikkatle) is uncommon and can sound marked or poetic.

Why is it formu and not formı/formü?

Accusative harmony picks one of -ı/-i/-u/-ü based on the word’s last vowel:

form → last vowel is back rounded o, so choose -u → formu. No buffer y is needed because the stem ends in a consonant.

Could I drop the accusative and just say duyuru or form?

Only if the object is non-specific/generic:

duyuruyu/formu = a particular one (the one we both know).
duyuru/form (no suffix) = nonspecific or generic (“an announcement,” “forms in general”). In this instruction, the objects are specific, so the accusative is appropriate.

How would I say this to one person informally?

Use the 2nd singular imperative:

Lütfen duyuruyu dikkatle oku, ardından formu doldur. You can drop lütfen to make it more direct, or keep it to be polite.

Are there other formal alternatives to ardından?

Yes, stylistic variants include:

akabinde (very formal)
sonrasında (neutral/formal) All work like ardından in this context:
… okuyunuz, akabinde/sonrasında formu doldurunuz.