Learn Hardcore Czech: Můj syn dnes spí dobře. - Today my son is sleeping well.

Můj syn dnes spí dobře. – Neutral: a simple statement of fact.
Dnes můj syn spí dobře. – Emphasizes dnes (today), e.g. compared to other days.
Můj syn spí dnes dobře. – Slight emphasis on dnes or on the combination spí dnes; still natural, though a bit less neutral than the first.

Czech tends to keep the subject–time–verb–manner ordering in neutral sentences, but shifting elements earlier in the sentence is a common way to emphasize them.

Why is it Můj syn, and not something like Mého syna?

Because můj syn is the subject of the sentence, so it appears in the nominative case.

Můj syn – nominative (who is sleeping?) → My son (subject)
Mého syna – genitive/accusative (of my son / my son as an object)
- e.g. Vidím mého syna. – I see my son.

In this sentence, you are saying who is sleeping well, not referring to him as an object, so nominative (můj syn) is required.

How does the possessive pronoun můj change with different genders and cases?

Můj is the masculine singular nominative form. It changes to agree with the gender, number and case of the noun it modifies. Very briefly for singular nominative (the basic dictionary form):

můj syn – my son (masculine animate)
můj dům – my house (masculine inanimate)
moje / má dcera – my daughter (feminine)
moje / mé auto – my car (neuter)

In other cases it changes more, for example (masculine animate):

Nominative: můj syn – my son (subject)
Genitive: mého syna – of my son
Dative: mému synovi – to/for my son
Accusative: mého syna – (I see) my son
Locative: o mém synovi – about my son
Instrumental: s mým synem – with my son

In Můj syn dnes spí dobře, we only need nominative, so můj.

Why is it dobře and not dobrý at the end?

Because dobře is an adverb (answering “how?”), while dobrý is an adjective (describing a noun).

spí dobře – he sleeps well (how does he sleep? → adverb)
dobrý syn – a good son (what kind of son? → adjective)

If you said Můj syn dnes spí dobrý, it would be wrong, because dobrý must describe a noun, not the verb spí.

Where is the verb “to be” in this sentence? In English we say “is sleeping”, but in Czech there is just spí.

Czech does not use a separate auxiliary verb “to be” for the present continuous the way English does. The present tense covers both English:

is sleeping (present continuous)
and
sleeps (simple present).

So:

Můj syn dnes spí dobře. – can mean both
- My son is sleeping well today.
- My son sleeps well today.

You only add je (is) for sentences like:

Můj syn je unavený. – My son is tired. (linking verb + adjective)
but not for simple actions like spí (= sleeps / is sleeping).

Is dnes an adverb or a noun? Does it change form?

In modern Czech, dnes functions as an adverb of time meaning today. As an adverb, it does not decline (it keeps the same form in all contexts).

So you always say dnes, no matter how it is used in the sentence:

Můj syn dnes spí dobře. – My son is sleeping well today.
Dnes je pondělí. – Today is Monday.
Co dnes děláš? – What are you doing today?

What is the difference between dnes and dneska?

Both mean today, but there is a slight stylistic difference:

dnes – more neutral, slightly more formal or standard.
dneska – more colloquial, often used in everyday spoken Czech.

You can say:

Můj syn dnes spí dobře. – perfectly standard.
Můj syn dneska spí dobře. – sounds a bit more casual, conversational.

Grammatically they behave the same way; both are adverbs and do not decline.

Can I move dobře before spí, like Můj syn dnes dobře spí? Does it change the meaning?

Yes, Můj syn dnes dobře spí is also correct. It slightly changes the rhythm and emphasis:

Můj syn dnes spí dobře. – neutral; focus is simply that his sleep is good today.
Můj syn dnes dobře spí. – can put a bit more emphasis on dobře spí as a unit (that he is indeed sleeping well, maybe in contrast to normally sleeping badly).

Both are natural; Czech often allows both verb–adverb and adverb–verb order.

How would I make this sentence negative?

To make it negative, add ne- directly in front of the verb:

Můj syn dnes nespí dobře. – My son is not sleeping well today.

In Czech, the negative is usually formed by prefixing ne- to the verb:

spí → nespí
You keep everything else the same (word order can still be flexible, of course).

How do I turn this into a yes–no question, like “Is my son sleeping well today?”?

For yes–no questions, Czech usually keeps the same words and structure, and relies on intonation (rising tone). One natural option here:

Spí můj syn dnes dobře? – Is my son sleeping well today?

Other acceptable variants with slightly different emphasis:

Můj syn dnes spí dobře? – My son is sleeping well today? (can sound like checking/confirming).
Spí dnes můj syn dobře?

Written questions are marked with a question mark; spoken questions rely on rising intonation on the verb or at the end.

How do you pronounce Můj, and what is that ů sign?

Můj is pronounced approximately like [muːj] in IPA, similar to “mooy” in English, but with a short j at the end.

About ů:

ů represents a long u sound, like ú.
ú is mostly used at the beginning of words (e.g. únor, ústa).
ů is used inside words (e.g. dům, kůň, můj – historically from uo).

So in můj, the ů is just a spelling convention; phonetically it’s a long u: múj → [muːj].

Can I say something like Spí se dnes dobře to mean “People sleep well today / One sleeps well today”?

Yes, but it means something different from the original sentence.

Můj syn dnes spí dobře. – My son sleeps well today. (personal subject)
Dnes se spí dobře. or Spí se dnes dobře. – Literally “It sleeps well today”, idiomatically “People sleep well today / One sleeps well today”. This is an impersonal construction using se.

So:

If you want to talk specifically about your son, use the personal form: Můj syn dnes spí dobře.
If you want a general statement (no specific subject), use Dnes se spí dobře.