What ties someone to a race?

First and foremost, I want to quickly define Race the way Dictionary.com does in verbatim.
Race: a group of persons related by common descent or heredity.
Furthermore, I'd like aknowledge how terrible of a misconception that it. Who are we to decide what defines a race? While watching The Human Stain, I realized that Coman was considered a colored person not only for being a jew, but because his family was a "colored" family. Though he himself didn't look "colored" at all, (and I use the term loosely as there is no true meaning that correctly justifies it being used for describing what ethnic group a person belongs to), He was still bound to that title and couldn't escape it. It's interesting to see how he lies on the registration card in the navy, he hesitates to put a racial belonging and then opts to put white and is immediately accepted.
Moreover, what exactly defines a race? Isn't it Ironic how most documents nowadays have completely redifined what it means to belong somewhere? There are sections that say "African American", "White", "Hispanic or Latino", "Pacific Islander", or "Other". There are different documents who take it a step further and separate "Hispanic or Latino" from "Mexican". As far as I know, White is a color and Pacific Islander is not a race, it's a region. And as far as colors go, I'm a yellowish crisp brown color, if you compare my skin color to a "light-skinned" person, you can argue i'm mixed. Asians usually have a similar skin complex to Caucasian and American people, point being, the way our government tries to classify people can be very inert and ignorant.
The Human Stain portrays various different jabs at different racial issues. The Jew who is constantly attacked and accused of racism by others in the University to get him fired or drive him to resignation. The "White" ex-military man who does as he pleases and has no serious punishment, (If any). The negro (who also happens to be the jew) who is told to lie about being negro when going to box and when signing for the navy. Ultimately what ties us down to a specific race?
If we go by color and heredity, it can be argued that I am a mixed person like many more from different countries or ethnic backgrounds and yet they still are considered black by the white people, and vise versa white by the black people. I am still considered hispanic, Asians are not considered white.
Or should we focus on our descent and roots? Wouldn't white people have a variety of descents and bloods? Ranging from English and Swedish to Irish, Danish, German, French, Austrian, Finnish, and etc. So where exactly does race fit in? how are people truly defined? By country or region? By color? By descent? What is the "proper" way to classify people? Are we not all just the Human Race?