They might be able to claim US citizenship at birth, depending on how long your sister lived in the US before their birth and her marital status at the time of giving birth, and her ability to prove that she lived in the US for the required number of years. See
http://travel.state.gov/law/citizenship/citizenship_5199.html
If they don't qualify for citizenship at birth, she'd have to file I-130 for each of them (and I-485, if they're inside the US) to get green cards for them. Upon green card approval they'd become citizens once they're living in the US in her custody.
Once their citizenship is established, she can apply for proof of citizenship in the form of a US passport and/or citizenship certificate (N-600).
If you have more questions about this, ask in the
US citizenship section.