We generally use into and onto to talk about movement.

The ball rolled into the goal. (NOT The ball rolled in the goal.)
She poured the tea into the mug. (NOT She poured the tea in the mug.)
How did the cat get onto the roof?

Note that the prepositions in and on are usually used to talk about position. However, after verbs like throw, jump, push and put, in and on can be used to talk about movement.

He jumped into the pond. (OR He jumped in the pond.)
He threw his hat onto the roof.
Throw another log on the fire.

Out of

Out of is the opposite of the preposition into.

She ran out of the room. (NOT She ran out the room.) (NOT She ran out from the room.)
She ran into the room.
He took the letter out of his pocket.

To

To is used for movement or direction.

She goes to school by bus. (NOT She goes at school by bus.)
I went to Canada to see my father.
We went to Marcel’s for coffee.

No preposition is used with verbs of movement and the noun ‘home’.

She went home. (NOT She went to home.)
They drove home. (NOT They drove to home.)

But we say: She went to the market and She went to school, not She went market and She went school.