Známe písně, například tuto.

In Czech, znát and vědět both relate to knowing, but they are used differently.

• znát = to know, be familiar with
• vědět = to know a fact, to know that, to be aware

So:

• Známe písně = We know songs / We are familiar with songs
• Víme, že... = We know that...

Because the sentence is about being familiar with songs, známe is the correct verb.

Známe is the 1st person plural present tense form of znát.

So it means:

• we know
• we are familiar with

A few related forms:

• znám = I know
• znáš = you know
• zná = he/she/it knows
• známe = we know
• znáte = you (plural/formal) know
• znají = they know

Because písně is the accusative plural of píseň (song).

The verb znát takes a direct object, and direct objects are usually in the accusative case in Czech.

• singular: píseň
• plural nominative/accusative: písně

So:

• Známe písně = We know songs

For this noun, the plural nominative and plural accusative happen to look the same: písně.

Because the meaning is:

• We know songs, for example this one.

The first part talks about songs in general, in the plural.
Then tuto points to one specific example from that group.

So the structure is basically:

• Známe písně = We know songs
• například tuto (píseň) = for example this (song)

The noun píseň is omitted after tuto, but it is understood.

Tuto is the accusative singular feminine form of tato (this).

Because the hidden noun is píseň, and píseň is:

• feminine
• singular
• functioning as a direct object here

the demonstrative must match it:

• nominative: tato píseň = this song
• accusative: tuto píseň = this song

Since the noun is omitted, only the pronoun remains:

• například tuto = for example this one

So tato would be nominative, but here Czech needs the accusative form tuto.

Yes. This is very common.

Czech often omits a noun when it is obvious from context. In English, we often add one:

• this one
• that one

Czech can simply use the demonstrative form by itself:

• tuto = this one
  (with the understood noun píseň)

The full version would be:

• Známe písně, například tuto píseň.

But that sounds more repetitive. The shorter version is natural.

Například means for example.

It is used to introduce an example:

• Známe písně, například tuto. = We know songs, for example this one.

Its position is fairly flexible, but this placement is natural. You may also see it in slightly different places depending on emphasis.

For example:

• Známe například tuto píseň. = We know, for example, this song.
• Známe písně, například tuto. = We know songs, for example this one.

In your sentence, it introduces a specific example from the broader category písně.

Yes. Here například tuto is added as an example to the main statement, so the comma helps separate that extra explanatory part.

• Známe písně, například tuto.

This is similar to English punctuation in:

• We know songs, for example this one.

In short, the comma marks například tuto as a parenthetical example.

Yes. That would be more colloquial.

• tuto is standard and somewhat more formal/written
• tuhle is common in everyday spoken Czech

So:

• například tuto = standard, neutral
• například tuhle = more conversational

Both mean for example this one, with an understood feminine noun like píseň.

Because the grammar matches.

Píseň is:

• feminine
• singular
• accusative in this context

And tuto is also:

• feminine
• singular
• accusative

So Czech listeners naturally connect tuto with the omitted noun píseň from earlier in the sentence.

If the omitted noun were masculine or neuter, the form would be different.

Roughly, písně sounds like PEES-nyeh.

A few helpful notes:

• í is a long ee sound
• sně is pronounced together, with ně sounding like nyeh
• stress in Czech is almost always on the first syllable, so: PÍS-ně

So the whole word is approximately:

• PÍS-nyeh

The exact Czech sound is a bit softer than an English approximation, but PEES-nyeh is a good start.