In many contexts when the meaning is 'to suppose', the two words are interchangeable: e.g. I assume/presume you are coming to the party. But, as the Pocket Fowler's Modern English Usage (Ed. Robert Allen. Oxford University Press, 1999) points out, 'Fowler (1926) maintained that there is a stronger element of postulation or hypothesis in assume and of a belief held on the basis of external evidence in presume.' The Oxford English Dictionary definitions are very similar. Assume is 'to take for granted as the basis of argument or action'; presume is 'to take for granted, to presuppose, to count upon'. There is a faint suggestion of presumptuousness about presume.
The New Oxford Dictionary of English which is based on recent usage evidence, provides these definitions:
assume suppose to be the case, without proof.
presume suppose that something is the case on the basis of "probability"; take for granted that something exists or is the case.
http://www.askoxford.com/asktheexperts/faq/usage/assume?view=uk
Assume has a variety of meanings. It basically means "to take up or on oneself," "to suppose or take for granted," "to pretend," or "to be taken up." The noun form is assumption.
Presume is related to and similar to assume, but it has the sense of doing it beforehand. It means "to dare or venture without prior knowledge," "to assume as believable without direct proof," "to take as a premise, subject to further proof," or "to behave arrogantly or overconfidently." The noun form is presumption.
A presumption is often taken up or assumed to be true until proven otherwise, as presumed innocent. Sometimes it has the sense of behaving in a superior manner, as in to presume upon someone. Presumption often has the sense of blind overconfidence, or going beyond the limits of proper manners. Presumptive means "based on reasonable grounds of evidence" as in presumptive heir. Presumptuous means "unusually confident or bold, often arrogant," or "foolhardy."
To assume suggest taking by one's own will or power for good or evil, right or wrong. If he assumes a position that is not rightfully his, he has arrogated or usurped it. A person can assume office either lawfully or unlawfully. When a debater assumes something, he or she may take it for granted without explaining it. If a person takes to himself character traits or a position he does not posses, he pretends to or affects the character he is assuming. A smooth talker often assumes something to be true that would be challenged if directly stated. When people claim something, they assert that they have a right to it. When they assume it, they take it.
The adjective assumed means "taken for granted" or "fictitious." When used as an adjective, assuming means "arrogant," its opposite, unassuming is more common. Something that is assumable is something that can be taken, as an assumable loan.
http://englishplus.com/grammar/00000304.htm
In other words, you should not assume things when thinking or planning. You should check details and ask questions.
You can, therefore, use the word assume when speaking or writing because you are, in fact, checking. The person you are writing or speaking to is supposed to set you straight if your assumption is wrong.
I assume he will be at the meeting. (You expect the reader/listener to inform you if your assumption is wrong.)
I presume he will be at the meeting.
If the person is important to your meeting, you should never “assume” he will be there. You should check by writing or speaking.
