#His master saw that Yahweh was with him

This means that the master saw how Yahweh was helping Joseph. AT: "His master saw that Yahweh was helping him" (See: [[:en:ta:vol1:translate:figs_idiom]])

#that Yahweh prospered everything that he did

"Yahweh caused everything that Joseph did to prosper"

#Joseph found favor in his sight

"To find favor" means to be approved by someone. The idiom  "in his sight" refers to a person's opinion. Possible meanings are 1) AT: "Potiphar was pleased with Joseph" or 2) AT: "Yahweh was pleased with Joseph" (See: [[:en:ta:vol1:translate:figs_idiom]])

#He served Potiphar

This means that he was Potiphar's personal servant.

#Potiphar made Joseph manager over his house, and everything that he possessed

"Potiphar put Joseph in charge of his household and everything that belonged to Potiphar"

#put under his care

When something is "put under someone's care," it means that the person is responsible for it's care and safe-keeping. AT: "he had Joseph care for" (See: [[:en:ta:vol1:translate:figs_metaphor]])