Finding a place to stay in Singapore is a big topic for any new arrival. I'll give some general hints here - others may add from their experience:
Rents in Singapore are high and volatile. Check the current market rate before looking for a place!
There are sublet rooms (limited privacy!), HDB apartments (govenmentally subsidized housing, 2 - 4 bedrooms), Condos (private apartments, often with amenities, 2 - 5 bedrooms) and landed houses (rare and expensive).
There are almost no 1-bedroom apartments (called "Studios") available and the few cost more than comparable 2-bedroom units!
Most rental places are fully or partially furnished. Sometimes it is possible to negotiate with the landlord that some pieces of furniture will be added or removed. The furniture will be usable, but don't expect anything high-class, valuable or looking nice!
Rental contracts are almost always fixed-term for a year or, more commonly, two years. Finding a place for a shorter period is very difficult, below six months even legally impossible. If you come for a shorter time, you are limited to hotels, hostels and serviced apartments (which cost more).
You can find "For Rent" ads on Internet classified ads sites. Google will help you!
The Singapore rental market is mostly in the hands of property agents, who have a well-deserved shady reputation for bad services and less than honest dealings. Be careful!
Agent fees are (by law) to be paid by whoever engaged the agent. If an agent advertises a place for rent, he must have been engaged for this by the property owner or landlord. If you rent such a place, you don't need to pay the agent a fee - in theory, but agents use lots of tricks to make you engage them even without you noticing it. For example: You contact an agent about a property he advertised, he tells you that one is already taken, but offers to look for similar places for you, you say yes - Wham: You engaged the agent for a property search and have to pay his fee!
Agent fees are freely negotiable (by law). One month rent per year rental contract is a common starting point for negotiations. Any agent who tells you that rates are fixed is not honest. By right, an agent contract (in writing) should be signed when you engage him, but this is seldom enforced.
It is possible to find a place to stay without agent, but it takes a lot more time and effort. However, the better deals are usually without agent (and on top of that you may save the agent fee).
If your employer or school offers accommodation (e.g. in a hostel), take it - it is almost always a better deal than what you can find on the open market!