Daná metoda funguje dobře.

Because metoda is a feminine singular noun, and the adjective has to agree with it.

• daný = masculine singular
• daná = feminine singular
• dané = neuter singular / plural in some contexts

Since metoda is feminine, the correct form is daná metoda.

Here, daná is being used like an adjective.

Historically, it comes from the verb dát (to give) and is related to a past/passive participle, but in sentences like this it often behaves simply as a normal adjective meaning something like:

• given
• particular
• specified
• the method in question

So in this sentence, daná metoda means something like the given method or that particular method.

Because it is the subject of the sentence.

The sentence structure is:

• Daná metoda = the subject
• funguje = the verb
• dobře = an adverb describing how it works

In Czech, the subject of a normal declarative sentence is usually in the nominative.

Funguje is the 3rd person singular present tense form of fungovat (to work, to function).

It is singular because the subject, metoda, is singular.

So:

• já funguji / funguju = I work / function
• ty funguješ = you work
• on/ona/ono funguje = he/she/it works

Since metoda is it in English, Czech uses funguje.

Yes, absolutely.

In Czech, fungovat is used very naturally not only for machines and devices, but also for:

• methods
• systems
• plans
• rules
• relationships
• solutions

So metoda funguje dobře is perfectly normal Czech and means that the method works well, is effective, or functions well.

Because dobře is an adverb, and it modifies the verb funguje.

You are describing how the method works:

• funguje dobře = works well

If you used dobrá, that would be an adjective, and it would describe a noun, not the verb.

Compare:

• dobrá metoda = a good method
• metoda funguje dobře = the method works well

That is a very common distinction in Czech, just like good vs well in English.

The order Daná metoda funguje dobře is the most neutral and natural one.

But Czech word order is fairly flexible, so other versions are possible depending on emphasis:

• Daná metoda funguje dobře. = neutral
• Dobře funguje daná metoda. = more marked; emphasizes well
• Funguje dobře daná metoda. = possible in some contexts, but less neutral

Even though the order can change, the basic meaning stays clear because Czech endings show grammatical relationships.

Yes, and that is often very natural.

There is a nuance:

• tato metoda = this method
• daná metoda = the given method, that specific method, the method in question

So daná is often used when the method has already been identified by context, while tato points to it more directly as this one.

In many situations, both can work, but they are not always exactly identical in tone.

It is pronounced roughly da-naa, with stress on the first syllable, as in virtually all Czech words.

A rough pronunciation guide for the whole sentence:

• Daná = DA-naa
• metoda = ME-to-da
• funguje = FUN-gu-ye
• dobře = DOB-zhe (the ř sound is special and difficult for learners)

Approximate full pronunciation: DA-naa ME-to-da FUN-gu-ye DOB-zhe

If you want to sound natural, remember that Czech stress is normally on the first syllable of each word.

Yes, very common.

You often see daný / daná / dané in:

• academic writing
• technical writing
• formal explanations
• instructions
• analytical texts

For example:

• daný problém = the given problem
• daná situace = the given situation
• dané řešení = the given solution

So Daná metoda funguje dobře sounds quite natural, and slightly more formal or analytical than a simpler everyday sentence.

Because Czech does not need a separate verb like to be here.

The main verb is funguje (works / functions), so the sentence is complete as it is.

English says:

• The given method works well.

Czech says the same thing directly with one finite verb:

• Daná metoda funguje dobře.

There is no missing is. The sentence already has its full verb.