Find a nanny who encompasses your values and can teach your children something. Make sure this person has at least one year's experience working as a household domestic worker. Otherwise they do not qualify for the required documentation. Nannies from China, India or the Philippines also do not qualify.
Apply to the Department of Labor for a labor certification. Fill out and file the permanent employment ETA Form 9089. The nanny can not be offered a temporary or part time job or they will not be admitted to the United States. On this form you will describe job duties, wages, training, experience and other qualifications that the potential immigrant possesses. There are directions to help you with this form online as well.
Petition U.S. Citizen and Immigration Services for a visa on behalf of the nanny after you receive a labor certification. Fill out an I-140 form, which is a petition for alien worker form, and file it, following instructions and remembering to send in the fee with it.
Follow the conditions of the visa carefully, and you will be able to have a foreign nanny without much more hassle.