1- Use am/is/are supposed to when something is planned, arranged, expected or said in the present or future. It can also be used when something is not allowed.
Eg: "I'm going to buy his book. It's suposed to be very good."
" I'm supposed to give a conference in Berlin tomorrow."
" Are you supposed to finish the project today?" Yes I am.
" He is not supposed to be here now"
"You are not supposed to speak Turkish in an English class.
2- Use was /were supposed to when you are expected to do something in the past but could not do it :
Eg: "The exam was supposed to start at 10.00, but the teacher was late."
"They were supposed to call before they go, but they didn't.
Watch a video on Youtube about be supposed to