You may refer to the following links
https://www.rom.gov.sg/reg_info/rom_solemnisation.asp
https://singaporelegaladvice.com/law-articles/civil-marriage-singapore-procedure-register-solemnise/
https://singaporelegaladvice.com/law-articles/can-a-muslim-marry-a-non-muslim-in-singapore/
Do note difference between non-Muslims and Muslims marriage.
after u file, have to wait at least 21days n within 3 months