Full details (including application forms, applicable fees and procedure) for application of Singapore Citizenship can be found at the website of Immigration & Checkpoints Authority (ICA).
Application for Singapore Citizenship can ONLY be submitted online at ICA's website.
Applicants may wish to note that all male Singapore Citizens by birth or registration and Permanent Residents (PR) are liable for National Service (NS) when they reach the age of 16½ years. They are required to serve 2 years of full-time NS and up to 40 days of NS every year until the age of 50 for officers or 40 for the others. Young Singaporeans who are accompanying their parents on overseas ventures must also discharge their NS obligations even if they have lived and studied away from Singapore for a period of time. This is regardless of whether they have taken up another citizenship. More information on NS requirements can be found in the MINDEF Homepage.