Ukradená peněženka patří této paní.

Because patřit means to belong to, and the person something belongs to is put in the dative case.

• tato paní = nominative = this lady
• této paní = dative = to this lady

So after patří, Czech uses the dative:

• Peněženka patří této paní.

A useful thing to notice: paní often looks the same in the singular, so the case is mainly visible in tato → této.

Because ukradená agrees with peněženka.

Peněženka is:

• feminine
• singular
• nominative

So the adjective/participle must also be feminine singular nominative:

• ukradená peněženka

Compare:

• ukradený telefon = masculine
• ukradené auto = neuter
• ukradená peněženka = feminine

It is originally a passive participle from the verb ukrást (to steal), but in this sentence it works like an adjective meaning stolen.

So for a learner, the simplest way to think about it is:

• ukradená peněženka = a stolen wallet

Grammatically, it behaves like an adjective and changes its ending to match the noun.

Because it is the subject of the sentence.

The sentence answers the question:

• What belongs to this lady?
• The stolen wallet.

So peněženka is the thing doing the grammatical job of the subject, which is why it is nominative.

Patří is the 3rd person present tense form of patřit.

Here it means belongs:

• peněženka patří = the wallet belongs

It matches the subject peněženka.
A small detail: in Czech, patří is also the 3rd person plural form, so the same form can mean belongs or belong, depending on the subject.

Because Czech has no articles.

English says:

• the stolen wallet
• this lady

Czech just says:

• ukradená peněženka
• tato / této paní

Definiteness is usually understood from context, word order, or words like ten, ta, to, tento, tato, toto.

Yes. Czech word order is fairly flexible because case endings show the grammatical roles.

This version is natural and neutral:

• Ukradená peněženka patří této paní.

But you could also say:

• Této paní patří ukradená peněženka.

That version puts more focus on této paní.
So the meaning stays basically the same, but the emphasis can change.

A few important pronunciation points:

• á, é, í are long vowels, so they are held a little longer:

  • ukradená
  • této
  • patří

• ř in patří is a special Czech sound with no exact English equivalent.
  A rough beginner approximation is something like rzh, but that is only approximate.

• Czech stress is usually on the first syllable of each word:

  • Úkradená
  • PEněženka
  • PAtří
  • TÉto
  • PAní

So patří is roughly pronounced something like PA-trzhee, though the real Czech ř takes practice.

Because paní is one of those nouns whose singular form is often the same in several cases.

So in:

• tato paní
• této paní

the noun paní stays the same, while the demonstrative changes and shows the case.

That is very common in Czech: sometimes the adjective/demonstrative makes the case clearer than the noun itself.