If your brother is under 21 years old than it can be done in less than a year. If your brother is older than 21 than it wil take about 5 years. She needs to file form I-130 with proof of the relationship, such as a birth certificate and proof of her U.S. citizenship. The current fee is $420.00.
If you still find the process confusing, you mother may want to hire an immigration attorney who can do it for her.
You can find more information here http://www.uscis.gov/USCIS/Resources/A1en.pdf.