Learn Hardcore Turkish: Siz lütfen formu doldurunuz, ardından sıradaki danışmana geçiniz. - Please fill out the form, then proceed to the next consultant.

Siz adds respectful direct address and can emphasize “you.”
-unuz/-iniz is the second-person plural imperative ending, used for polite/formal address (even to one person). You could omit either and still be correct:
Lütfen formu doldurunuz, ardından … geçiniz.
Siz lütfen formu doldurun, ardından … geçin. The version given is very formal/polite, typical of written instructions.

What’s the difference between "doldurun" vs "doldurunuz" (and "geçin" vs "geçiniz")?

They’re both second-person plural imperatives. The forms with -iniz/-unuz are more ceremonious and common on signs, announcements, and official instructions. The shorter -in/-ın/-un/-ün forms are still polite/formal but sound more neutral and conversational.

Lütfen bekleyin. (neutral polite)
Lütfen bekleyiniz. (very formal/polite, sign-like)

Why is "formu" in the accusative case?

Because it’s a definite, specific object (“the form” that is known in the context). In Turkish, definite direct objects take the accusative:

Definite: formu doldurunuz.
Indefinite: bir form doldurunuz (“fill a form,” any form). Leaving out -u here would sound odd because a specific form is meant.

Why is it "formu" (with -u), not "formi" or "formı"?

Accusative -i follows 4-way vowel harmony. The last vowel of “form” is o (a back, rounded vowel), so the accusative becomes -u:

o/u → -u
a/ı → -ı
e/i → -i
ö/ü → -ü Hence: form + -u → formu.

What exactly is "ardından," grammatically and in usage?

It’s an adverb meaning “after that/afterwards.” It comes from ardı (“back/rear/after”) + ablative -ndan.
It can also be a postposition taking a genitive complement: işlemin ardından (“after the process”).
Here it refers anaphorically to the previous action (“after that”), linking the two commands in sequence. You could also say:
Sonra … (afterwards, less formal)
… doldurduktan sonra … (after doing X; more explicit, neutral)

Could I replace "ardından" with "sonra" or "daha sonra"? Any nuance?

Yes:

Sonra is very common and neutral: “… formu doldurun, sonra sıradaki …”
Daha sonra is “later (on),” which can sound a bit less immediate.
Ardından is slightly more formal/written and clearly means “right after that” here.

Is the comma before "ardından" correct? Could I use a period or a semicolon?

All are acceptable. Turkish often uses a comma to link short, related imperatives:

… doldurunuz, ardından …
… doldurunuz; ardından …
… doldurunuz. Ardından … The period makes the sequence most explicit; the comma is common in concise instructions.

How is "sıradaki danışmana" built, and what does "-ki" do?

sıra (order/turn/line) + -da (locative) + -ki (adjectivizer) → sıradaki = “the one that is in the sequence,” i.e., “the next.”
danışman-a is dative (“to the consultant”). The suffix -ki forms adjectives meaning “the one in/at/on …”:
soldaki kapı = the door on the left
odadaki masa = the table in the room
sıradaki müşteri = the next customer

Why is "danışmana" in the dative (-a/-e)?

Because geçmek with the dative means “to move on/proceed to, switch to”:

kasaya geçin (proceed to the cashier)
1. kata geçin (go on to the 3rd floor) So: danışman-a geçiniz = proceed to the consultant.

Is "danışmana geçmek" natural? Could I use something else?

Yes, it’s natural in service contexts. Alternatives:

sıradaki danışmana ilerleyiniz (proceed/advance to the next consultant)
danışman masasına geçiniz (proceed to the consultant’s desk)
danışmana yöneliniz (head toward the consultant; more formal)

What’s the difference between "danışman" and "danışma"?

danışman = a consultant/advisor (a person).
danışma = the information/help desk (a place/function). So “danışmana geçiniz” sends you to a person; “danışmaya geçiniz” sends you to the info desk.

Could I drop "Siz"? Would that change the meaning?

You can drop it with no change in basic meaning:

Lütfen formu doldurunuz, ardından … Including Siz gives an added sense of respectful direct address or emphasizes “you (as opposed to someone else).” It’s optional.

Why not just say "ve" (“and”) instead of "ardından"?

“Ve” simply adds another command without ordering them. Ardından encodes sequence (“after that”), which is important here. Without it, you’d lose the clear order of steps.

Could I phrase this as a softer question instead of imperatives?

Yes. Using the aorist + question is a common polite request:

Lütfen formu doldurur musunuz, ardından sıradaki danışmana geçer misiniz? This sounds like “Would you please…?”—very courteous in speech.

Is "sıradaki" the same as "sonraki"?

They overlap but aren’t identical.

sıradaki = “the next in line/turn/order” (queue/sequence context).
sonraki = “the next/later one” in a more general series, not necessarily about a queue. Here, sıradaki danışman is the idiomatic choice.

What’s the nuance between "geçmek" and "gitmek" in this context?

gitmek = to go (to a place), neutral motion.
geçmek (-(y)e) = to move on/proceed/switch to the next step or station. In multi-step instructions, geçmek is idiomatic: you’re transitioning to the next point in a process.