The process of getting an American citizenship and the right to live in US is called Naturalization. When the applicant wish getting all the rights that Americans have including voting, pension and — that is the most important — obtaining the USA passport, he applies to USCIS.
All citizens of the United States who are 21 and older can apply with a petition for their siblings (sisters and brothers) to reside in the USA, holding a Greed Card. Kids that have one common parent (at least) are also referred to siblings. To be called a sibling of a US citizen a person might not be related to him/her by blood.
When a foreign souse of an American intends to enter the USA with her kids, children are issued CR2/IR2 Visa. This visa for a children is given only for unmarried persons under 21 years old. Stepchildren can be also given this visa even when they are married, but only in case when the marriage was registered before the child marked his 18th birthday.
Important information: Marriages between the same sex persons Now spouses (the USA citizens or residents) that have the same sex and kids have all the rights as opposite sex persons who are married. They are also eligible getting family-based visas and immigrate to the USA. These visas are given on I-140 or I-130 petitions previously approved. Check FAQ sections to get more facts about it.