.......purchasing and installing Dawnguard? I understand Dawnguard upgrades werewolves and vampires stats/abilities and changes vampire eye color. So if you install DG after playing a character who was already a vamp or wolf, how does it work? Please explain it to me.

Theres nothing to explain. you will have the upgrades as soon as you install Dawnguard.

Same way. It just upgrades them with the new stuff.