How do crystals give superman powers?

They don't.

Kryptonian technology is based upon growing and manipulating crystals.

Superman recharges himself directly through solar energy because of his physiology.

Superman recharges his powers in yellow sunlight. Red sunlight is bad for him. Kryptonite crystals affect him differently depending on the color of the kryptonite. Green is the most common, and can kill him. I think the rest have some extremely strange effects, though the only other one I distinctly remember is that pink kryptonite changes a Kryptonian's sexuality.

It turns the man of steel gay. No lie. Look it up. It's actually in the comics.

They reflect the light from the sun because he is recharged by the sun and he made the fortress of solitude so that the light would specifically hit him all at once recharging his power

No, crystals do not give Superman powers. His powers are innate, and charged by the sun. That is to say, a yellow sun. A red sun takes his powers away and makes him like a normal person, and a blue sun supercharges him. I don't know what a white dwarf would do. Probably weakens him, too.

In fact, a specific kind of crystals WEAKENS him, namely kryptonite. Kryptonite is a mineral or class of minerals.

http://dc.wikia.com/wiki/Kryptonite