Reduction using sodium borohydride
Sodium borohydride is a complex unit made from the let's call it molecule $\ce{BH3}$ and the salt $\ce{NaH}$. Group 3 compounds like boron only have what we call an electron sextett instead of an octett. That makes them good Lewis acids, hence they tend to react with Lewis bases to form adducts. A famous example is the $\ce{H3B-NH3}$ adduct. In your example the hydride anion $\ce{H^-}$ is the Lewis base that forms an adduct with $\ce{BH3}$ to give $\ce{Na[BH4]}$. This means that at least one $\ce{H}$ in $\ce{[BH4]^-}$ can be somewhat easily removed again. The others tend to react as well but let's just call the $\ce{BH3}$ unit a stable molecule and assume it's a combination of $\ce{BH3}$ and $\ce{NaH}$. It's just a good way to store this hydride-anion so that it can be easily removed again. So once it sees your carbonyl group that has a positive partial charge on the carbonyl carbon (as the more electronegative oxygen pulls the electrons closer to itself) it can attack there as nucleophile. As you drew it already the double bond will turn to a single bond giving a negative charge on the oxygen. 

Next you have to assume that $\ce{B}$ and $\ce{O}$ form quite stable bonds, hence the formation of a $\ce{B-O}$ bond is somewhat favored. And of course once the hydride ion is at the carbon we end up with an electron sextett on the boron again. Therefore it's the same thing, the carbonyl oxygen with an extra negative charge behaves like a strong Lewis-base again forming an adduct with the $\ce{BH3}$ unit. 

This is later treated with water or acidified water to get the alcohol. To the question on the final product. I once talked to a boron chemist about that. He doubts that all four hydrogens will act as reducing agent under normal conditions. It's more likely that they will get hydrolyzed during workup. 

Edit: Thinking about it. If you aren't sure about what attacks first you could probably also consider a transition state. I drew in the arrows here but you shouldn't do that (although you see it too often). I guess this would just be an alternative view on the reaction.