Children of US Citizens and Permanent Residents (including children born in and out of wedlock, stepchildren and adoptive children) are eligible to apply for permanent resident status.

1. IR/CR-2, IR-3/4, F-1/3, F-2A, F-2B
IR-1/2:Unmarried children under the age of 21 of US Citizens
IR-3/4:Orphans adopted abroad/domestically
F-1:Unmarried children above the age of 21 of US Citizens
F-2A:Unmarried children under the age of 21 of US Permanent Residents
F-2B:Unmarried children above the age of 21 of U.S. permanent residents
F-4:Married adult children of US Citizens
Among above categories, F categories subject to quotas. Latest Visa Bulletin please see: www.travel.state.gov 

2.General Case Procedure
First, file I-130 form along with other supporting documents to the USCIS. After that, the petitioner will receive I-797 approval notice and the USCIS will transfer the case to NVC (National Visa Center). For categories which do not need to wait for quotas, NVC sends out fee payment bill once finished processing materials. For categories which need to wait for quotas, NVC sends out Visa fee payment bill when the petitioner's priority date is close to becoming current . After the payment, NVC will send out package 3.
Then, finish package 3 and send it back to NVC. NVC will transfer the case to US consulate appointed after background-check (If pass it, package 4 will be send to you). Around this time, the beneficiary need to get medical examination and be prepared for the consulate interview.
Finally, if the interview goes well, the beneficiary will be approved to have his or her immigrant visa.

3.Documents
Form I-130
Application Letter
Primary Documents:
1.Certificate of Naturalization, Certification of Citizenship or Certificate of U.S. permanent resident status
2. Unexpired US passport;
3. Birth Certificate showing birth in the U.S.;
4. Report of birth abroad of a U.S. citizen (FS-240)
Secondary Documents:
1. Affidavits sworn by persons who are familiar with the events of birth of the petitioner
2. School records (preferably from the first school) showing the date of admission to the school, the child's date and place of birth, and the names and places of birth of the child's parents.
3. Census records
4. Military proof

Proof of Relationship: In all situations, the parents have to provide their children's birth certificates. If the child was born in wedlock, the parents have to provide marriage certificate, household registration, documents that can prove termination of previous marriage and so on. There are other situations such as children born out of wedlock, step child, adopted child, siblings of the adopted child, different situations needs different documents to prove/meet various standards.