Yes, his pants are longer than what you can buy in a store. Store bought pants go down to about the bottom of the calf, normally.
Socks are pulled up to just below the knee, and the pants are over top of them. Just like you would wear normal pants, with long socks.
I think a lot of the Yankees actually wear finger socks. that is where the socks are made like a glove with each toe going into its own sleeve. Hideki Matsui brought a pair over from Japan, and they liked them. At least that is the rumor I have heard. I have actually never seen a pair being used. But, I have never hung out with the Yankees either.
The most common thing I have seen is a player first puts on a pair of very thin socks, called sanitaries. Then the team sock. Both go right up to the bottom of the knee. I have never seen a player wear socks on the outside of the pants.
The 2 styles of wearing the pants are high or low. A-Rod has the low look. His pants cover his socks. The high look, my favorite, is simply the pants pulled up to the knee, exposing the socks. All pants come with an elastic band around the bottom, that holds pretty tight. You can place the bottom of your pants anywhere, and they will hold pretty well. I have never seen a pair of pants being worn high, have the legs fall down in the middle of a game. The elastic works really well.
Here is an animated *.gif, actually showing A-Rod sporting both styles.http://www.swingtraining.net/clips/arod-06-07-load-st.gif