Here's a woman who explained how she obtained a second citizenship.
She already has a US citizenship and purchased a second citizenship to St. Kitts and Nevis. She hired a lawyer who lives in St. Kitts, took a physical exam, supplied college transcripts, her Social Security number, and a lot of other information. The fee was $150,000 not including legal fees and other fees. It took about 8 months for the citizenship, and another 4 months to get a passport for St. Kitts and Nevis.