If you mean a NEW car then the first thing is to read the owners manual for the service intervals EVEN IF the car has an automatic reminder.
I, being of an age that remembers when even new cars had faults... Check the tires, oil and coolant every week for the first month and after that the oil and coolant every month forever. ( Like French polishing a piece of furniture). Check the tires every month Feb thru Oct and every week Nov thru Jan. Tire pressures drop off a lot in the fall as the weather gets colder.
Remember that new tires and brakes need a couple of hundred KMs to "break in"
If the car is brand new this week then buy some winter tires.