How does a Wizard use books and words to draw on the weave? It's never actually explained, they just do it.
A portfolio is just a divine decree that details scope and power. It's connected to the whole tablets of fate deal, which are the tablets kept by Ao that detail the how the world exists, the balance between good evil law chaos, and what the duties of the deities are.
Think of a portfolio basically as a pass to the weave, which is just raw energy. Gods have access the weave according to the power of their portfolios, and they can re-direct some of that energy to their followers or champions. It apparently doesn't take a lot of effort to do so (at least, according to the Faiths and Pantheons book).
On a related point, the twin world of Toril, Abeir, has no weave, and it's not possible to be a Cleric in that world the same way as in Toril.
