When do you use no and wa in Japanese?

'No' can mean both '~'s' and 'of'.

Example 1: Hikaru no yume. (Hikaru's dream)

Example 2: Watashi no yuujin (A friend of mine)

Note that example 2 shows 'watashi' which means 'I'.

'No' can also mean to, with, in, at, from, etc...

'Wa' is just a particle, which means something that marks the noun.

Example 3: Watashi wa hon wo yomimasu. (I read a book.)

Example 4: Watashi no heya ni ikkou. (Let's go to my room.)

Note that example 4's 'no' means possession. Hence, 'I' possesses the room.

I'll not explain what the other Words mean and how you can use it since that's not your question.