By how much does taking an antibiotic decrease the effectiveness of birth controle. she took one antibiotic pill and has been on birth control for a wile. what should she do?

Usually no worries: The current thinking is that except for rifampin, other commonly-used antibiotics (such as doxycycline and many others) do not alter the effectiveness of birth control pills. This is likely presuming a person is not sick with vomiting or rapid diarrhea, or some other condition that decreases the absorption of a swallowed pill. One can look up: http://www.ncbi.nlm.nih.gov/pubmed/12063491