How can I make my parents U.S Residents?

If your parents are already here in the country and they entered with a visa or on parole, they would not have to leave if you applied for their permanent residence. You would file form I-130 relative petition for both of them (two forms) and they would concurrently file I-485 adjustment of status applications. Both petitions and applications would be filed at the same time with fee and relating documentation to that Chicago lockbox of USCIS. The process takes approximately 7 months and your parents may or may not be interviewed depending upon the decision of USCIS. Due to the limitations of the lawyers.com forums, Alan Lee, Esq.’s (the firm) participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting the question. No attorney/client relationship is or shall be construed to be created hereby. The information provided herein by the firm is general and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice, nor as the basis for making any decisions of legal consequence.

If your parents are in the US without authorization and have been for over a six months, they will need a waiver.  You first need to petition for them using form I-130 (one for each of them), then, once that is approved and ready for processing, you may apply for the waiver (which requires proving extreme hardship to a US citizen spouse or child).  If the waiver is approved, they would need to travel outside the US to get an immigrant visa in their passports, but they would return as permanent residents.  The process will take at least a year.