If the friend's only immigration problem is that she overstayed her visa, marrying a US citizen would allow her to adjust status while remaining in the US. (Before she can become a US citizen, she must adjust status to become a legal permanent resident.)
There are many possible bases why a person cannot adjust status. You can search prior posts at this site for the most common bases. Search for "adjust status" in the search box.
Your friend should consult an attorney since the resolution of her situation likely will depend on the specific facts of her case.
Your question is quite compounded. If your friend entered legally and has proof of her legal entry, she may be eligible to obtain legal permanent residence through her soon to be US Citizen husband. The application process requries several forms and supporting documentation. Marrying a US citizen does not erase or eliminate any legal impeidments your friend may have; however, as noted, her legal entry is in her favor.
Your friend would also be eligible to apply for US citizenship either 3 or 5 years after obtaining her legal permanent residency. The number of years she must wait to apply for citizenship depend on her circumstances after her marriage to the USC. I would encourage your friend to consult with an immigration attorney and discuss in detail her immigration history and current situation.