The parents of a U.S. citizen who is at least age 21 are considered "immediate relatives," and therefore eligible for a green card, allowing them to live and work in the U.S. -- at least in theory. A stumbling block for some parents of U.S. citizens is that they are already living in the United States unlawfully, and have already done so for six months or more, which makes them inadmissible.
Other issues to consider are that the child will be required to prove that his or her household income is sufficient to support their family and their parents at 125% or more above the U.S. poverty level, and that they must truly intend to live in the U.S. -- a green card is not a travel document, and if they stay outside the U.S. too long, the immigration authorities may come to notice that that is where they truly "live," and deny reentry.
Let's look separately at the situations of parents who are living in the U.S. unlawfully, those living in the U.S. lawfully, and those who are living in another country.
Various circumstances can lead to a situation where the child is a U.S. citizen but the parent an undocumented immigrant. Perhaps the parents came to the U.S. unlawfully, or on a visa that has since expired, and gave birth to the child in the United States. Or perhaps the parents brought the child from another country, and the child somehow qualified for a green card while the parents did not, then eventually applied for U.S. citizenship (naturalization). Or perhaps the child invited his or her parents to visit in the U.S., and the parents never got around to leaving the United States.
In any of these cases, the parents need to understand that, if their unlawful stay was at least 180 days long, they have become "inadmissible" to the U.S. for three years; and if the unlawful stay was one year long, they have become "inadmissible" to the U.S. for ten years. No waiver is available to parents of a U.S. citizen.
What does this ground of inadmissibility mean in practice? If the parents perform the final step of applying for a green card (in particular, the personal interview with an immigration official) in another country, they will not be allowed to return to the U.S. for three or ten years. But luckily for some parents -- namely the ones who entered on a visa or through the visa waiver program -- they will not be required to leave the U.S., but can stay and receive their green card through the procedure known as "adjustment of status," attending their interview at an office of U.S. Citizenship and Immigration Services (USCIS). This is true even if they overstayed the visa. The only catch is that they cannot have misused the visa, that is, obtained it simply in order to come to the U.S. and get a green card.
For more on the differences, see Consular Processing vs. Adjustment of Status.
Parents who entered the U.S. without inspection are not allowed to adjust status unless they fall into a rare exceptional category.
If parents of a U.S. citizen happen to be living in the U.S. on a valid visa, they should be able to adjust status as the immediate relative without trouble. That means submitting all their paperwork to, and attending their interview at, an office of USCIS. The only likely hurdle is if they committed visa fraud by applying for the visa with the idea of gaining U.S. entry in order to adjust status. In other words, if they, for example, applied for a tourist visa, they are supposed to have truly intended to be tourists, and only later decided to apply for a green card.
For parents who are living outside the U.S., and haven't done anything in the past to make them inadmissible, the application process to get a green card through a U.S. citizen child should be fairly straightforward. They should expect to attend their visa interview at a U.S. consulate in their home country before coming to the U.S. on an immigrant visa. Upon entry, they become lawful permanent residents.
The process of getting a green card for parents depends on whether they will be adjusting status or going through consular processing.
For adjustment of status, it basically involves submitting both an I-130 visa petition (prepared by the child petitioner, sometimes called the sponsor) along with the parents' own application on Form I-485, with supporting forms and documents to USCIS. One of the important supporting forms is one that the child will also need to submit, known as Form I-864, the affidavit of support promising that the child will reimburse any government agency from which the parents receive need-based assistance. These materials are submitted all at once by mail to USCIS, after which the parents will be called in for fingerprinting, and finally an interview.
For consular processing, the child starts off the processing by submitting an I-130 visa petition to USCIS. After that is approved, the case will be transferred first to the National Visa Center (NVC), and then to an overseas U.S. consulate. The parents will fill out various State Department forms, and the child will need to submit USCIS Form I-864. Although the forms are slightly different, in the end, the information collected is the same. The parents will attend an interview at a U.S. consulate or embassy in their home country.
If the U.S. citizen child wishes to sponsor an adopted or step-parent, both are possible. However, the marriage that created the step-relationship must have occurred prior to the child's 18th birthday.