Learn Polish: Wczoraj zszedłem z tej śliskiej skały. - Yesterday I went down this slippery rock.

The first z is a prefix on the verb, changing the base motion into a perfective verb meaning to go down. The second z is a separate preposition meaning from or off of. In Polish, it is very common to pair a z- prefixed motion verb with the preposition z to explicitly mark the starting point of the downward motion.

I know the infinitive for to go down is zejść. Why does it start with z- here instead of ze-?

The prefix is technically z-, but it sometimes adds an -e- to make pronunciation easier before tricky consonant clusters. In the masculine past tense zszedłem, the cluster zsz is manageable in Polish so the e is dropped. However, a female speaker would say zeszłam because the zszł cluster would be too hard to pronounce, so the e comes back!

Why are the words tej śliskiej skały in the Genitive case?

They are following the preposition z. When z means from, off of, or down from, it always forces the following noun phrase into the Genitive case. Remember not to confuse this with the preposition z meaning with, which takes the Instrumental case.

Why does the adjective śliskiej end in -iej rather than just -ej?