Działanie kompostownika jest proste.

A word-for-word breakdown is:

• działanie = operation, functioning, how something works
• kompostownika = of the composter / compost bin
• jest = is
• proste = simple

So the whole sentence means something like:

• The operation of the composter is simple
• How the composter works is simple
• The composter works in a simple way

Depending on context, działanie can sound a bit formal or technical, like operation or functioning.

Because it is in the genitive case.

The base form is kompostownik = composter / compost bin.
After the noun działanie in this meaning, Polish often uses another noun in the genitive to mean the operation/functioning of something.

So:

• kompostownik = a composter
• działanie kompostownika = the functioning of the composter

This is similar to English the operation of the composter.

Działanie is in the nominative singular.

It is the grammatical subject of the sentence:

• Działanie kompostownika = the functioning of the composter
• jest proste = is simple

So the structure is:

• subject: działanie kompostownika
• verb: jest
• description/predicate adjective: proste

Because proste agrees with działanie.

The noun działanie is:

• singular
• neuter
• nominative

So the adjective must also be:

• singular
• neuter
• nominative

That gives proste.

Compare:

• plan jest prosty = the plan is simple, masculine
• metoda jest prosta = the method is simple, feminine
• działanie jest proste = the operation/functioning is simple, neuter

In normal present-tense Polish, jest usually stays in sentences like this.

So:

• Działanie kompostownika jest proste = correct and natural

If you remove jest:

• Działanie kompostownika proste

that sounds incomplete or unnatural in standard Polish.

This is different from Russian, for example, where the present-tense to be is often omitted. In Polish, with a sentence like this, jest is normally required.

The standard, neutral order is:

• Działanie kompostownika jest proste

But Polish word order is fairly flexible, so other orders are possible for emphasis, for example:

• Proste jest działanie kompostownika
• Jest proste działanie kompostownika

These are less neutral and may sound literary, marked, or context-dependent.

For a learner, the safest version is the original one: Działanie kompostownika jest proste.

Polish does not have articles like English a and the.

So kompostownik can mean:

• a composter
• the composter

and the exact meaning depends on context.

In this sentence, English will usually use the:

• The operation of the composter is simple

but Polish does not need a separate word for that.

A rough pronunciation guide for an English speaker is:

• Działanie ≈ דזשா-WAH-nyeh or jwah-WAH-nyeh
• kompostownika ≈ kom-po-stov-NEE-ka
• jest ≈ yest
• proste ≈ PROS-teh

A few useful pronunciation points:

• dz in działanie is a voiced sound, like the start of judge but smoother
• ł is pronounced like English w
• nie at the end of działanie sounds roughly like nyeh
• j in Polish sounds like English y in yes

A more Polish-like approximation of the whole sentence is:

jwah-WAH-nyeh kom-po-stov-NEE-ka yest PROS-teh

Yes, in many contexts it can be.

Działanie is a broad noun that can mean:

• operation
• functioning
• action
• the way something works

So Działanie kompostownika jest proste can naturally mean:

• The functioning of the composter is simple
• How the composter works is simple

If you wanted a slightly less technical wording, other options might be possible depending on context, but działanie is perfectly good and natural.

Yes, it is grammatical and natural, especially in informative or educational language.

It sounds like something you might read in:

• a guide
• an instruction sheet
• a school text
• an explanatory article

It has a slightly neutral-to-formal tone because of działanie. In everyday conversation, someone might also say something more direct, depending on context, but this sentence itself is completely normal.