I'm thinking of taking the day off tomorrow.

Literal

Tomorrow [topic-は] day-off [object-を] take-[volitional-おう] [quotative-と] thinking.

休みを取ろうと思っています wraps the volitional 取ろう in ~と思っている, creating a softened 'I'm thinking of doing X' — less committed than ~つもりだ. The ~ている marks the thinking as an ongoing state of consideration.