Learn Hardcore Korean: toyoire sijangeseo gwaireul sayo. - On Saturday, I buy fruit at the market.

에 is a particle that marks a specific point in time, similar to on in English. So 토요일에 literally means on Saturday—it tells us when the action happens.

What’s the difference between 에 and 에서, and why is 시장에서 used here?

에 marks a destination or a point of existence (e.g., 학교에 가요 = “I go to school”).
에서 marks the location where an action takes place (e.g., 공원에서 놀아요 = “I play at the park”). Since buying fruit is an action happening at the market, we use 시장에서 (“at the market”).

Why does 과일 have 을 attached? What does 을 mean?

을 is the object particle used after a noun ending in a consonant. It marks 과일 as the direct object of the verb 사요. If the noun ended in a vowel, you’d use 를 instead.
Example:

책을 읽어요 (I read a book)
사과를 먹어요 (I eat an apple)

Why is the verb written as 사요 instead of 사다?