Descartes undermines his customary 'world-view' by doubting its very foundations. He aims to build up a certain understanding of the world from first principles. To do this he supposes that there is nothing in the world. External things are 'nothing but the deceptive games of (his) dreams' created by a deceiving demon.
Descartes realises that he cannot be deceived about his own existence: '…one must come to the considered judgement that the statement 'I am, I exist' is necessarily true every time it is uttered by me or conceived in my mind.'
Seeking to gain further certainties Descartes considers an external object - a block of wax - but because he has no direct access to the wax itself (but only those ideas that fill his mind as he considers it) his 'own existence follows with certainty, but not that of the wax'.
Since Descartes does clearly and distinctly perceive the world then, because God is perfect and cannot be a deceiver, God's existence would assure him of the real existence of the material world.
Descartes proves the existence of God. (It is 'impossible that I should exist… having the idea of God in me - unless God in fact does exist' he declares.)
God is perfect and therefore cannot deceive. This would seem to imply that we cannot make errors. However humans are finite creatures and our 'knowing' is limited. Errors occur when we employ our wills to make judgements with incomplete knowledge.
The ideas that Descartes has of external things are sometimes distinct, sometimes confused. He is fully convinced by things that are 'clearly and distinctly' perceived. The most certain are 'things pertaining to arithmetic, geometry or, in general, to pure and abstract mathematics'.
Speaking of the idea of an external object (say, the block of wax) he distinctly imagines '…the extension of its quantity… length, breadth and depth… the thing's various parts… certain sizes, shapes, positions… movements… (and) durations.' He continues: 'I find within me countless ideas of things that, although perhaps not existing anywhere outside me, still cannot be said to be nothing… e.g. when I imagine a triangle… its nature, essence, or form is completely determined… I did not produce it and it does not depend on my mind.'
Descartes proves the existence of God a second time. (The idea of God requires his existence. In his case (alone) it is part of his essence to exist - otherwise he would not be perfect.)
Descartes continues: 'I plainly see that the certainty and truth of every science depends upon the knowledge of the true God… now it is possible for me to know certainly and fully countless things - both about God and other intellectual matters, as well as about all corporeal nature, which is the object of pure mathematics.'
God's goodness requires that I am not in fact deceived when I clearly and distinctly perceive external objects. I can rightly conclude that 'corporeal things exist'. I have a body with which I am 'so to speak, mingled together', though I am 'truly distinct' and 'can exist without it'.