Citizenship and Immigration Services needs to approve form I-130 (the document that recognizes that your claimed relationship is valid) to the National Visa Center. Once the National Visa Center is notified, then the National Visa Center will contact you to begin the next part of the process.
National Visa Center
The National Visa Center will contact your sponsor and request an immigrant visa fee bill. Then they will request an affidavit of support from the petitioner, showing that she can support her relative financially when they enter. They will also request information about the alien. Once all of this information is provided, the National Visa Center will forward the file to the US Embassy in your relative's home country.
US Embassy -- processing and first interview
The US Embassy will set your relative for an initial interview in his home country. At that interview the alien file will be reviewed, and they will tell your relative that he is inadmissable - because he stayed in the US for more than one year without permission after you were 18. You will be informed that this can be cured with a waiver on form I-601 based on extreme hardship to immediate family members. Your relative will be given a second interview date to deliver those applications.
Your relative, if deported, also needs to complete form I-212,permission to return following deportation. If the I-601 is granted, the I-212 will be granted.
Deliver the Waiver or Waivers
Your relative will return with form I-601 (and maybe I-212) and all supporting evidence. At his home country, in most cases they will accept the waiver, and then it will be forwarded to the central waiver adjudications center, which will decide the case in nine to twelve months.
If the waiver is denied, there is an appeal that could take two years before being complete.
Wait for Approval!
Once the waiver is approved, the Embassy contacts your relative to schedule an appointment where he can come and take his lawful permanent residence and the packet he needs to enter the United States.