As a part of ASEAN, Singapore citizens are exempt from Vietnam visa for 30 days. For stay of longer than 30 days, Singaporean nationals may have 2 options: Visit Vietnam embassy in Singapore or apply for a visa on arrival to Vietnam from Singapore online. Singaporean citizens may apply for both tourist and business visa to Vietnam for the stay of 1 to 6 months from Singapore. Please check this link for visa fee for Singaporean citizens.
All the information for getting a visa from Vietnam embassy in Singapore can be found here: http://www.vietnamembassy-singapore.org/

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