State laws and insurance companies' guidelines vary regarding if there is a grace period to put insurance on a new car. Your state may or may not offer a grace period for coverage to be placed on a vehicle. If the new car is your first vehicle or it will be an additional vehicle on your policy, thus not replacing a car already on your policy, then likely there is no grace period and insurance will need to be placed on the vehicle before you drive off the dealership's lot. If you are financing the purchase, the lender will require that you buy a policy with comprehensive and collision coverage.
If instead the new car is replacing a car that was on the policy, such as a car you traded in, some insurance companies will extend the old vehicle's insurance onto the new car for a few days so you have time to come in and change the information, others may not allow this. Normally it will depend upon what state law dictates. Check with your state insurance regulatory body to find out what grace period, if any, the state allows.
If you are transferring coverage from a car you traded in, this transfer of coverage will be the same type of coverage you had on your trade in vehicle. So if the car you took in only had liability and the car you drove away from the dealership requires physical damage coverage on it, than you will not be covered for that "full coverage" until you add it onto the vehicle.
Be sure to inform your insurer of the new vehicle as soon as possible, if you do not notify the company of the change of vehicle within the given time, allowed either by state law or the insurance company, then your new car will not have coverage on it.
It is best, if feasible, to set up the policy before you pick up the car or as soon afterwards as possible. If you do not have a current insurance policy to cover a new vehicle, you can start here by getting a car insurance quote.