One of the best way to visit the Serangoon area is to take the MRT subway trains via the North-east line (see website below). This is a direct, fast ,cheap and convenient way and the instructions are in English so no problems.
If you want to visit the famous Little India area of Serangoon, alight at either the Little India station or Farrer Park station (the latter is nearer to the famous Mustafa department store, as well as the City Square Mall).
You can get to Serangoon road by bus, MRT, or taxi. If your hotel is near then just walk.
If you take the bus, fares depend on distance travelled. You will have to pay when you get on. If you don't know the fare the driver will tell you but he doesn't give change so keep small coins in your pocket.
You can alight at Little India Station and take exit C or E out. Once you are out of the station, there is a map around to show you the places around Little India.
I will encourage you to take exit C, you will see shops when you come out of the station, walk towards yr left and round the flats. Voila, you will smell the Indian spices and flowers as you walk towards the main road. Towards the right will be the Tekka Wet Market and towards yr left will be the Hindu Temples and the eateries.