You can say 'I suppose' when you want to express slight uncertainty.

You can say 'I suppose' or 'I don't suppose' before describing someone's probable thoughts or attitude, when you are impatient or slightly angry with them.

You can say 'I don't suppose' as a way of introducing a polite request.

You can use 'do you suppose' to introduce a question when you want someone to give their opinion about something, although you know that they are unlikely to have any more knowledge or information about it than you.

You can use suppose or supposing before mentioning a possible situation or action. You usually then go on to consider the effects that this situation or action might have.

If you suppose that something is true, you believe that it is probably true, because of other things that you know.