I am a 20 year old full-time student and I have been providing over half of my mother's support and I am wondering if I can claim her as my dependent

Do you have any income? Does mom have any income? That is the crucial question here. Not how old you are.

I am 20 years old and a full-time student and I have 2 jobs that is totaling over 12,000. My mother gets a check for $516.00 monthly and I needed to know how old does one have to be to claim my mother and head of household

Your age is not an issue. For your mother to be your dependent, you must provide more than half of your mother's support for the year, and her income must be less than $3,650. Since your mother gets a check for $516/mo, that means her income is a bit over $6K/year. So she is not a "qualifying relative," and you can not claim her as a dependent. You also can't file as HoH. See Pub 501, pages 11-12. Note that there is an exception if your mother is disabled that would allow you to claim her.
http://www.irs.gov/pub/irs-pdf/p501.pdf

Thank you very much for this much needed info

Also, Social Security also NOT considered income for the purposes of the dependency test, and I suspect that $516 IS Social Security.