Expect to pay around $3,000 for a modest 2 bedroom place and around $4,500 for a decent 3 bedroom place.
Here's the best site I know of which has details of nearly all places
SingaporeExpats
I signed a 2 year lease on a 3 bedroom place out near the airport last February (2007) for $2,300 a month. The current going price for the same place is $3,800 and it's nothing special. 3 bedrooms but basic in a reasonable area, but quite a way from the centre.
Landlords will want you to sign up for a minimum of 2 years and will want 2 months deposit, plus rent in advance, i.e. you need to pay 3 month's rent before you move in.
The housing market shot up last year (see above comment regarding my rent) and seems to be stalling at present. There's a lot of construction work currently going on and prices are expected to come down later this year / start of next year when a lot more new accommodation hits the market.
Commission for agents varies, I had to pay 1 month's rent to mine because the rental price was below $2,500 a month. I was told that had I rented a place for more than this, then the landlord would have paid it. Also, be careful as they do things a strange way here - it's not very transparent. There's a central database which all agents use and it may not (almost certainly not) the case that the same agent represents the landlord and you. This means 2 lots of commission !! Make sure you become familiar with the way it works before you agree to anything, the locals love ripping off the foreigners !!
Good luck.