Good news, and it is worth stating plainly because a number of agencies sell a "Singapore visa" to Nepali travellers who do not need one: Nepal is not on Singapore's visa-required list. You can travel for a social visit without applying for a visa at all.
At a glance
Visa needed: No — Nepal is not on the ICA visa-required list
Length of stay: Up to 30 days, granted by the immigration officer on arrival
What you do need: SG Arrival Card, submitted online within 3 days before arrival
Cost: Nothing. The SG Arrival Card is free
Watch out for: Anyone charging you for a "Singapore eVisa"
Fees
There is no visa fee, because there is no visa. The SG Arrival Card is free on the ICA website. If someone quotes you a Singapore visa fee, ask them which visa, on which official page.
Visa types
Social visit (no visa) — Up to 30 days. Tourism and visiting family. Entry and length of stay are decided by the officer at the checkpoint.
Business visit (no visa) — Up to 30 days. Meetings and conferences. Carry the invitation and your company letter in case you are asked.
Student pass — Course length. Arranged through the Singapore institution via ICA before travel.
Work pass — Varies. Employer-sponsored and applied for by the employer in Singapore, not by you.
Documents required
Passport valid at least 6 months from arrival
SG Arrival Card submitted online within 3 days before you land
Confirmed onward or return ticket
Proof of accommodation in Singapore
Evidence of sufficient funds for your stay
Employment or study letter, in case the officer asks about your ties to Nepal
Before you apply
No visa is not the same as guaranteed entry
The immigration officer still decides. Have your return ticket, hotel booking and funds ready to show, and be able to explain your trip clearly.