Immigration
The officer normally grants the visitor a 14 or 30 day social visit pass. I'm not quite sure if there are instances where they give less than 14 days for tourists.
Transportation
MRT and LRT System Map can be found on each train station, however it is still advisable to have a map on hand. The link below will show you the map which you can print for your own reference.
There are designated stops for the buses, you can't just flag them anywhere. These vehicles are numbered.
The most expensive way of transportation is Taxi. Drivers provides receipt after each ride.
(Hindi po nangongontrata ang mga taxi dun. hehe!)
A singapore tourist pass which provides unlimited ride to train and buses can also be bought, but if you are to visit two sites a day, you won't get to maximize the S$8 per day fee. It will still be cheaper to buy a single journey ticket.
On every vehicle, the driver is on the right side so be careful when crossing the street, always look to your left and right.
Where to Stay
Of course there are lots of Hotel in Singapore, if you have enough money to spend, there's Fullerton Hotel, Meritus Mandarin and other big hotels waiting for you. But if you don't have much, you can try the backpacker's hostel ranging from S$20 to S$38 dollars (including breakfast). So always try to search the net for the most affordable one if you're on a tight budget, anyway you will always be out of your room.
The Food
Chips at Sentosa
Pasta Fusion & Venezia from Bugis Junction