Ať dobrovolníci třídí oblečení podle velikosti a čistoty.

Here ať is a particle used to express a wish, instruction, or indirect command about a third person.

So Ať dobrovolníci třídí... means something like:

• Let the volunteers sort...
• Have the volunteers sort...
• The volunteers should sort...

It is very common in Czech when you want to say that someone else should do something, not you directly.

Czech has normal imperative forms for you:

• Třiď! = sort! (singular)
• Třiďte! = sort! (plural/formal)

But there is no ordinary imperative form for he/she/they in the same way.
So Czech uses ať + present tense to express a third-person command or wish.

That is why you get:

• Ať dobrovolníci třídí... = Let the volunteers sort...

not a special separate imperative form.

Dobrovolníci is the nominative plural of dobrovolník (volunteer).

It is in the nominative because it is the subject of the verb třídí:

• dobrovolníci = the volunteers
• třídí = sort / are sorting

So literally, the structure is:

• Ať = let / may
• dobrovolníci = the volunteers
• třídí = sort

Třídí is the 3rd person plural present tense of třídit (to sort, classify).

Because the subject is dobrovolníci (the volunteers), the verb must be plural:

• dobrovolník třídí = the volunteer sorts
• dobrovolníci třídí = the volunteers sort

After ať, Czech normally uses this present-tense form to express the command/wish.

In Czech, oblečení is very often a collective or mass noun, meaning clothing or clothes in a general sense.

Grammatically, it is singular neuter, even though in English we often use the plural clothes.

So:

• oblečení = clothing / clothes

This is normal Czech usage.

Also, in this sentence oblečení is the direct object, but for this noun the nominative and accusative singular look the same, so the form does not change.

It is in the accusative singular, because it is the direct object of třídí:

• sort what?
• oblečení

For neuter nouns like oblečení, the accusative singular is often identical to the nominative singular, so the form stays the same.

The preposition podle means according to, by, or on the basis of.

A key grammar point is that podle requires the genitive case.

So:

• velikost → velikosti
• čistota → čistoty

That is why we get:

• podle velikosti a čistoty = according to size and cleanliness

They are both in the genitive singular, but they belong to different noun patterns.

• velikost is a feminine noun ending in -ost
• čistota is a feminine noun ending in -a

So their genitive singular forms are different:

• velikost → velikosti
• čistota → čistoty

Both are correct genitive forms after podle.

Here čistoty means cleanliness.

The noun is čistota, from the adjective čistý (clean).
In this sentence it refers to how clean the clothing is, so the idea is:

• sort the clothes by size
• and by degree of cleanliness / whether they are clean

It does not mean the action of cleaning.

Třídit is the imperfective verb, and that fits well here because the sentence gives an instruction about an activity or process:

• Let the volunteers sort the clothing...

Imperfective is commonly used for:

• ongoing activities
• general instructions
• repeated or process-oriented actions

A perfective verb would suggest a more result-focused meaning, such as finishing the sorting or sorting everything into final groups. Here the emphasis is simply on the task itself.

Yes. Czech word order is flexible, although the original sentence is very natural.

You could also hear:

• Dobrovolníci ať třídí oblečení podle velikosti a čistoty.

This gives a bit more emphasis to dobrovolníci.

But the original:

• Ať dobrovolníci třídí oblečení podle velikosti a čistoty.

is a standard and neutral way to express the instruction.

No. Czech has no articles like the or a/an.

So Czech simply says:

• dobrovolníci = volunteers / the volunteers
• oblečení = clothing / the clothing / clothes

The exact English article depends on context, but Czech does not mark that directly with a separate word.