Nejdřív vyplňte formulář, pak ho podepište.

Because these are imperative forms used for:

• more than one person: Fill out the form, then sign it.
• one person addressed formally/politely: like using you politely

So vyplňte = fill out! and podepište = sign! in the plural/formal imperative.

Compare:

• informal singular: vyplň, podepiš
• plural/formal: vyplňte, podepište

In Czech, the same -te form is used both for you all and for formal you.

This is mainly about aspect.

Czech verbs often come in pairs:

• vyplnit = to fill out, fill in completely (perfective)
• vyplňovat = to be filling out, to fill out repeatedly/habitually (imperfective)

And similarly:

• podepsat = to sign (perfective)
• podepisovat = to be signing / sign repeatedly (imperfective)

In commands like this, Czech usually prefers the perfective imperative when the speaker wants the action to be completed:

• vyplňte formulář = fill out the form
• podepište ho = sign it

So the sentence sounds natural because it tells someone to complete step 1 and then complete step 2.

Nejdřív means first, at first, or first of all in this kind of instruction.

In this sentence it introduces the first step:

• Nejdřív vyplňte formulář... = First, fill out the form...

Yes, it is very close to nejprve. Both are common and natural.

• Nejdřív vyplňte formulář.
• Nejprve vyplňte formulář.

Nejdřív often sounds a little more everyday and conversational, while nejprve can sound slightly more neutral or formal, but both work well here.

Formulář is the direct object of vyplňte, so it is in the accusative case.

But formulář is a masculine inanimate noun, and in the singular its accusative form is the same as its nominative form.

So:

• nominative: formulář
• accusative: formulář

That is why you do not see a change here.

Ho means it here, referring back to formulář.

So:

• pak ho podepište = then sign it

Grammatically, ho is the accusative singular pronoun. It can mean:

• him
• it for masculine nouns

Since formulář is masculine in Czech, Czech uses ho to refer to it.

Because ho is the normal unstressed object pronoun in everyday Czech.

For formulář, you could also theoretically use jej, but ho is much more common in ordinary speech and writing:

• natural: pak ho podepište
• more formal/literary: pak jej podepište

Why not to? Because to refers to neuter nouns, and formulář is masculine, not neuter.

So ho matches the gender of formulář.

Because short pronouns like ho usually have a fixed position early in the clause in Czech.

In pak ho podepište, pak comes first, and the short pronoun ho comes right after that, before the main verb:

• pak ho podepište

This is very natural Czech word order.

English says:

• then sign it

But Czech often places short pronouns earlier than English does.

Yes, but the original version is the most neutral and natural for instructions.

Standard, natural order:

• Nejdřív vyplňte formulář, pak ho podepište.

You may also hear or see variations, for example for emphasis:

• Formulář nejdřív vyplňte, pak ho podepište.
• Nejdřív formulář vyplňte, pak ho podepište.

These are possible, but the original sentence is the clearest everyday instructional style.

Very little in this sentence. Both mean then / afterwards.

So these are both fine:

• Nejdřív vyplňte formulář, pak ho podepište.
• Nejdřív vyplňte formulář, potom ho podepište.

Pak is short and very common in speech. Potom is also common and may sound just a little more explicit. In instructions, either works.

It is formal or plural, because of vyplňte and podepište.

So it could be said:

• to one person politely
• to several people

If you wanted to say it to one friend informally, you would normally say:

• Nejdřív vyplň formulář, pak ho podepiš.

So the original sentence is the kind of wording you might see in:

• official instructions
• customer service
• signs
• forms
• polite spoken instructions

The comma separates two coordinated command clauses:

• Nejdřív vyplňte formulář
• pak ho podepište

In English, you might also write this with a comma:

• First fill out the form, then sign it.

In Czech, the comma helps mark the pause between step 1 and step 2.

A rough guide:

• Nejdřív ≈ NAY-dzheerv
• vyplňte ≈ VI-pln-tye
• formulář ≈ FOR-moo-laarzh
• pak ≈ pahk
• ho ≈ ho
• podepište ≈ po-de-PISH-te

A few notes:

• ř in nejdřív is the famous Czech sound that is hard for English speakers. It is not exactly r or zh, but something in between.
• ň in vyplňte is like a softened n.
• Stress in Czech normally falls on the first syllable of each word:
  • NEJdřív
  • VYplňte
  • FORmulář
  • POdepište

You do not need perfect pronunciation immediately; these words will still be understood if your ř is not native-like.

Usually you should keep ho here, because it clearly tells us sign it.

• pak ho podepište = then sign it

If you say only pak podepište, it sounds incomplete unless the object is obvious from the context or is mentioned elsewhere.

So in this sentence, ho is the natural choice because it links the second action directly back to formulář.