Question

How did michelangelo paint the frescoes of the sistine chapel?

Answer 1

This is an ambiguous question: if you meant with what medium and implements he painted, it would probably be animal hair brushes and fresco (paint applied to damp plaster).
He stood (not lying down, as is popularly believed) while painting on wooden boards hanging by the building scaffolding by ropes, so that he was close to the ceiling.