If you are driving to Tanglin Halt from the city, you can take the Ayer Rajah Expressway and go out at the Buona Vista exit near to the National University Hospital. Another way is to take the Pan Island Expressway and exit at Farrer Road. There is several big car parks at Tanglin Halt which are mostly empty most of the time, so it will be easy (parking is 50 cents per half hour on weekends, and free on sundays and public holidays).
If you are taking the MRT sub-way train, the nearest station to alight would be the Commonwealth station and the Tanglin Halt area is just next to the station (very convenient). As for local buses, you can take SBS bus number 62 from the city area directly to Tanglin Halt.