If you are planning to travel to the U.S., whether for a simple visit or the start of a brand new life, and wish to bring your children along with you, you will have to make sure they have their own visas.
While certain aspects of the application process might be a little simpler for young children than they are for adults, every traveler needs to have his own visa - even babies and toddlers.
One of the main distinctions in the visa path for children under 14, is that their legal guardian may attend the consular interview instead of them.
If you are planning to visit the U.S. as a tourist with your child, or your child will be traveling in alone (for example, to go visit a relative in the U.S.), you will need to demonstrate that their accommodation is provided for during their stay, and that they have enough funds available to cover their daily expenses. This can be as simple as an invitation letter from their U.S.-based point of contact, stating they will cover accommodation and travel expenses. Of course, if your child is traveling alone, they will need to carry a written letter of consent from one of their parents or a legal guardian.
Transit visas are only granted to children if they are traveling with a parent or legal guardian - so watch out before you book them a connecting flight through the U.S.!
As a holder of an F1, M1 or J1 visa as a student in a U.S. educational / vocational institution, your child would qualify for an equivalent F2/M2 or J2 visa as your dependent. In order to apply for one of these visas, you will only have to prove the relationship with the child and show that you already hold your student visa.
A parent who is already in the U.S. as a Legal Permanent Resident and who is looking to bring over their children to join them on a permanent basis can go through the IR-2 visa process in order to get them their own Green Cards. In order to be able to submit a petition for their visa, and act as their sponsor, you will have to have lived with your child for at least two years, before the date of the application - legal guardians need to have had legal custody for the same period of time.
An immigrant visa will certainly take more time than nonimmigrant entry permits to obtain, as you will have to demonstrate sufficient financial means to take care of your child and provide a stable life. However, the USCIS takes uniting families as one of their highest priorities, and this is particularly true with minor children joining their parents.
Overall, you should expect your child’s Green Card to be delivered around one year after the application if you are a U.S. citizen, and around 2 years later if you are a Green Card holder.