How I can apply petition for my mother who came visit me from her country

If your mother was lawfully admitted as a tourist (or similar status), she might be eligible to adjust her status to that of lawful permanent resident. Besides your relationship, there are many other eligibility factors to consider. Unfortunately your fact pattern does not provide the board with sufficient information to properly assess your mom's situation.

Please consult with and consider hiring an immigration attorney to represent your mother. The attorney should be skilled in family based visas. Attorneys who practice immigration law are practicing federal law and therefore you can hire an attorney from anywhere in the country (as long as he/she is licensed).