To become a Singaporean citizen you have to satisfy a number of requirements; this can often take a long period of time. After these are satisfied, other citizenships must be renounced before one can officially become a Singaporean.
There are several different types of people eligible to apply for citizenship:
Permanent Residents at least 21 years old, who have been resident on a permanent basis for 2-6 years
A Permanent Resident who has completed the National Service obligation
The spouse of a Singaporean who has been both married and a Permanent Resident for at least 2 years
A child born outside of Singapore with one of both parents holding Singaporean citizenship
The requirements to become a citizen differ depending on which type of eligibility the candidate fulfills (note: some documentation is only required if applicable to you personally):
Permanent Residents 21 and over
Completion of the Citizen Application form and the Annex form
Passport
A recent passport photo
Entry Permit Card/Re-entry permits
A Birth Certificate and Identity Card
Marriage Certificate/Divorce Certificate/Separation Deed
Education Certificates
Letter of employment from current employer and job details including pay, duration of employment and occupation
Income tax notice for the previous 3 years
History of CPF contributions for the last year
If the proprietor/partner/director of a company the latest balance sheet/profit and loss account
Death Certificate of any ex-spouses and proof of custody for and children from other marriages
Birth Certificate and Passport for any of these children
Entry Permit/Identity Card for children
Certificates for change of name
Foreign Citizenship Certificate and Foreign Identity Card
Adopted children of Singapore citizen(s)
For the Child
Recent passport photo
Identity Card, Birth Certificate, Passport
Certificates for change of name
Adoption Order
For the Parent(s)
Birth Certificate
Singapore Citizenship Certificate
Adoption Certificate
Passports for other children
Identity Card
Marriage Certificate
Educational Certificates
Passport
Death Certificate of any ex-spouses
Divorce Certificate/Separation Deed of ex-spouses
Custody Document
Letter of employment from current employer and job details including pay, duration of employment and occupation
Income tax notice for the previous 3 years
If the proprietor/partner/director of a company the latest balance sheet/profit and loss account
CPF contributions for the last year
Natural children of Singapore citizen(s)
For the Child
Birth Certificate
Passport
Recent Passport photo
Completion of the Citizen Application form
For the Parent(s)
Identity Card
Passport
Marriage Certificate
All minors who become citizens of Singapore by either descent or registration must take the Oath of Renunciation, Allegiance, and Loyalty within one year of turning 21. This consists of going into the Citizen Services Centre and taking the oath. If this is not done by the minors 22nd birthday, they will lose their citizenship immediately.
Both the citizenship application form and the Annex form, which are needed to apply for citizenship, can be found at http://www.ica.gov.sg.