Jak děti, tak rodiče se budou na oslavě usmívat, pokud bude na stole dobrý dort a čisté ubrousky.

It means both the children and the parents.

Here jak ... tak ... is a fixed Czech pair meaning both ... and .... So jak is not being used with its usual meaning how here.

Examples:

• Jak Petr, tak Jana přišli včas. = Both Petr and Jana arrived on time.
• Jak děti, tak rodiče = Both children and parents

Both are nominative plural forms, because they are the subject of the main clause.

• děti = children, nominative plural of dítě
• rodiče = parents, nominative plural of rodič

A learner often notices that děti is irregular. That is normal:

• singular: dítě
• plural: děti

And:

• singular: rodič
• plural: rodiče

Because the subject is plural: both children and parents.

So the verb agrees with a plural subject:

• děti a rodiče se budou usmívat
• literally: children and parents will smile / will be smiling

Even though the two parts are joined by jak ... tak ..., together they still make a plural subject.

Because usmívat se is an imperfective verb.

In Czech, the future of an imperfective verb is normally formed with:

• future of být = budu, budeš, bude, budeme, budete, budou
• plus the infinitive

So:

• budou se usmívat = they will be smiling / they will smile

This is the normal way to make the future of usmívat se.

Se is part of the verb usmívat se. You learn the verb together with it.

So the dictionary form is:

• usmívat se = to smile

As for position: se is a clitic, and Czech clitics usually go very early in the clause, often after the first stressed unit.

Here the first unit is:

• Jak děti, tak rodiče

So the sentence naturally continues:

• Jak děti, tak rodiče se budou ...

That is why you see se budou, not because se changes the meaning, but because Czech word order places it early.

This is mainly a matter of aspect.

• usmívat se = imperfective, ongoing or repeated smiling
• usmát se = perfective, one completed smile

So:

• Budou se usmívat.
  = They will be smiling / they will smile in a general or ongoing sense.

• Usmějí se.
  = They will smile once / they will give a smile

In this sentence, usmívat se fits well because it suggests a general cheerful atmosphere during the celebration.

Na oslavě means at the celebration or at the party.

Here na is used with the locative case to show location:

• na oslavě = at the celebration

The noun is:

• oslava = celebration
• locative singular: oslavě

Czech often uses na with events:

• na svatbě = at the wedding
• na koncertě = at the concert
• na večírku = at the party

So na oslavě is a very natural phrase.

Pokud means if, provided that, or as long as.

In many contexts it is close to jestli, but pokud can sound a bit more formal or more explicitly conditional.

So:

• pokud bude na stole dobrý dort...
• if there is / if there will be a good cake on the table...

Very roughly:

• pokud = if, provided that
• jestli = if, whether
• když = when, and sometimes if in more colloquial or repeated situations

In this sentence, pokud is a good, clear conditional choice.

This is a very common learner question.

You might expect plural budou, because there are two things:

• dobrý dort
• čisté ubrousky

But Czech often uses singular bude in a sentence like this because the structure is presenting what will be present somewhere, almost like English there will be.

So:

• pokud bude na stole dobrý dort a čisté ubrousky feels like:
• if there will be a good cake and clean napkins on the table

In this kind of presentational or existential wording, singular bude is natural.

A plural budou may also be possible in some contexts, but bude here is perfectly normal and idiomatic.

Because adjectives must agree with the noun in gender, number, and case.

• dort is masculine inanimate singular nominative
  → dobrý dort

• ubrousky is masculine inanimate plural nominative
  → čisté ubrousky

The form čistí is used for masculine animate plural, not masculine inanimate plural.

So:

• čisté ubrousky = correct
• čistí ubrousky = incorrect

Compare:

• čistí psi = clean dogs or honest/clean-living dogs depending on context, but grammatically masculine animate plural
• čisté stoly = clean tables, masculine inanimate plural

It is locative singular.

The noun is:

• stůl = table

After na meaning location, Czech uses the locative:

• na stole = on the table

Compare:

• na stole = on the table, already there, location
• na stůl = onto the table, movement toward it

So in this sentence:

• bude na stole = will be on the table

There are two important commas here:

1. Jak děti, tak rodiče ...
   Czech normally separates the two parts of this paired conjunction with a comma.

2. ..., pokud bude na stole ...
   The clause introduced by pokud is a subordinate clause, and Czech separates it with a comma.

So the commas help show the structure:

• jak ..., tak ...
• main clause + conditional subordinate clause

There is no comma before a čisté ubrousky, because that is just a normal coordination of two nouns: dort a ubrousky.