Learn Polish: Z tyłu domu jest ogród. - At the back of the house there is a garden.

Both are correct! Za domem uses the preposition za (behind) with the instrumental case. Z tyłu domu literally means "at the back of the house" and is just another very common way to express this. They are largely interchangeable, but z tyłu draws a bit more attention to the physical back area of the property itself.

Why is dom in the genitive case (domu)?

The phrase z tyłu acts as a compound preposition. Whenever you state what is in the back of something using z tyłu, the noun that follows it must take the genitive case. This conveniently mirrors the English word "of" in "at the back OF the house."

How exactly do the words z tyłu build the meaning "at the back"?

The noun tył means "the back" or "the rear." The preposition z here takes the genitive case (tyłu) and originally means "from." So literally, z tyłu means "from the back," but it has become the standard fixed phrase in Polish for "in the back" or "at the back."

Where is the word for "there" in the Polish sentence?

Polish doesn't use a dummy subject like "there" for "there is" or "there are." You simply use the verb jest (is) along with your subject (ogród). Notice that ogród is placed at the very end of the sentence; Polish often puts the most important new information at the end, which does the exact same job as "there is..." does in English.