Η περιποίηση του σκύλου θέλει χρόνο και υπομονή.

Because περιποίηση is a feminine singular noun, so it takes the feminine singular definite article η in the nominative case.

• η = the for feminine singular subjects
• περιποίηση = grooming / care

So η περιποίηση means the grooming or the care.

Because here the dog is not the subject. It means of the dog, so Greek uses the genitive case:

• ο σκύλος = the dog
• του σκύλου = of the dog / the dog’s

So η περιποίηση του σκύλου literally means the grooming of the dog.

Greek nouns change form depending on their grammatical role. This is called case.

σκύλος is a masculine noun of the common -ος type:

• nominative singular: ο σκύλος
• genitive singular: του σκύλου

In this sentence, the dog is showing possession or association, so Greek uses the genitive singular form σκύλου.

Yes, θέλω usually means I want / I want to, and θέλει literally means he/she/it wants. But in everyday Greek, θέλει is also very commonly used in the sense of:

• needs
• requires
• takes

So in this sentence, θέλει χρόνο και υπομονή means something like:

• requires time and patience
• takes time and patience

This is a very natural Greek usage.

Because the subject is singular: η περιποίηση.

Even though the whole subject phrase is η περιποίηση του σκύλου, the head noun is still περιποίηση, which is singular, so the verb must also be singular:

• η περιποίηση ... θέλει

If the subject were plural, the verb would also be plural.

They are in the accusative case because they are the direct objects of θέλει.

• χρόνος → χρόνο in the accusative singular
• υπομονή stays υπομονή in nominative and accusative singular, so the form looks the same

So:

• θέλει χρόνο = it needs time
• θέλει υπομονή = it needs patience

Because Greek often leaves out the article with nouns like time, patience, and other general or abstract things when speaking in a broad sense.

So:

• θέλει χρόνο και υπομονή = it takes time and patience

This sounds natural and general. If you added articles, it would sound more specific:

• θέλει τον χρόνο = needs the time
• θέλει την υπομονή = needs the patience

That would usually suggest some particular time or particular patience, not the general idea.

Yes. In this sentence, και simply links the two nouns:

• χρόνο και υπομονή = time and patience

It works very much like English and.

Yes, Greek word order is more flexible than English word order. The sentence as written is neutral and natural:

• Η περιποίηση του σκύλου θέλει χρόνο και υπομονή.

But Greek could also rearrange parts for emphasis, for example:

• Χρόνο και υπομονή θέλει η περιποίηση του σκύλου.

This would emphasize time and patience.
So the original order is the most straightforward one, but other orders are possible.

A rough pronunciation guide is:

i peripi-Í-si tu SKÍ-lu THÉ-li HRÓ-no ke ipo-mo-NÍ

A few useful notes:

• η sounds like ee
• ει in περιποίηση also sounds like ee
• ου in του and σκύλου sounds like oo
• θ in θέλει is like English th in think
• χ in χρόνο is a harsher sound, not exactly like English h

The stress marks in Greek show where the voice should rise slightly:

• περιποίηση
• σκύλου
• θέλει
• χρόνο
• υπομονή

No. Περιποίηση is a broader word. It can mean:

• care
• grooming
• treatment
• looking after someone or something

So it can be used for:

• a dog
• a person
• hair or skin care
• general care/attention

In this sentence, because it is followed by του σκύλου, it specifically means the dog’s grooming/care.