I started my period on May 20th and it started light and dark brown. On week two still light but regular color. What should I do?

I don't think it is anything to be too concerned about. The brownish discharge or smearing is usually an indictation of blood that is not fresh or old blood and the body is trying to cleanse the lining of the uterus and of course mostly the redish blood is your period. The brownish color has gone away and you are having a regular period as you wrote. If you are sexually active be concerned with the possibility of becoming pregnant if a child would be inwanted at this time.