We often use  'suppose' to mean 'imagine' or 'guess'
  • I suppose you'll be meeting Danielle when you go to Paris?
  • When you weren't there, I supposed you must have been held up.
  • I suppose you two know each other?
Notice that 'suppose' is not normally used in the continuous form. We do not usually say 'I am supposing'.
  • Now I suppose we'll have to do something else.
  • We're waiting for John and I suppose he must be stuck in traffic.
  • At this moment I suppose it doesn't matter.
Notice that for 'imagine not' or 'guess not' that we make 'suppose' negative, not the other verb.
  • I don't suppose you know where Mary is?
  • I don't suppose he'll do anything.
  • I don't suppose you  have a Nokia phone charger here?
When responding to an idea with 'suppose', you can use 'so' to avoid repeating the idea that has already been expressed.
  • Is Susan coming to this meeting? ~ I suppose so.
'Supposed to be' can be used to mean 'it is said/believed'.
  • The new James Bond movie is supposed to be excellent.
  • He is supposed to have been rude to Mark but I don't believe it.
  • It is supposed to be the best restaurant in town.
'Supposed to be' can also be used to talk about what is arranged, intended or expected. It is a bit like 'should'.
  • I'm supposed to get to work by 8.
  • John is supposed to turn off all the lights when he leaves.
  • I'm supposed to pay my rent on the first of the month.
  • It's not supposed to be here.
Often there is a suggestion that the action 'supposed to' happen does not actually happen.
  • I'm supposed to be there before 8 but I'm often late.
  • You were supposed to phone me.
  • I'm supposed to be getting on a plane to Tokyo at this very minute.
'Not supposed to' often suggests that something is not allowed or prohibited.
  • You're not supposed to smoke in here.
  • I'm not supposed to tell you.
  • We're not supposed to use the Internet for personal reasons at work.
'Suppose' can also be used as a conjunction to mean 'what if'. Notice that the verb which follows it is sometimes, but not always, put 'more in the past'.
  • Suppose we take the earlier train to Munich? It would give us more time there.
  • Suppose we took the plane instead? That would give us even more time.
  • There's nobody in reception to let our visitors in. Suppose I sit there until somebody comes?
  • I'm going to ask him for a pay increase. ~ Suppose he said 'no'? What would you do?