Learn Polish: Ten park miejski podoba się mojemu psu.

It uses the suffix -ski, which is one of the main ways to form relational adjectives (adjectives that define a category rather than a quality). Notice the significant stem change here: the root miast- softens and changes to miej- before adding -ski.

Why is the adjective miejski placed after park instead of before it?

Relational and classifying adjectives in Polish usually go after the noun they describe to create a specific term or category, such as park miejski for city park or municipal park. If it were a subjective descriptive adjective, it would typically go before the noun, like in ładny park meaning a pretty park.

Why is the phrase mojemu psu in the dative case?

The verb podobać się means to appeal to or to be pleasing to. It requires the entity experiencing the liking to take the dative case. So instead of my dog likes the park, the Polish grammar literally structures it as the park is pleasing to my dog.

What happens to the spelling of pies to get the dative form psu?

The noun pies meaning dog contains a fleeting e. When you decline it and add case endings, the e in the stem drops out. The root becomes ps-, to which you simply add the standard masculine dative ending -u.