How can a person without a car get a car insurance?

You can't as an insurance company needs to know what vehicle they are insuring and for what value.

If you are renting a car you will have a few different options to choose on what insurance you require. Even then you will not be allowed to hire the vehicle with no insurance.

When you are going to buy a car you can apply for cover once you have chosen a vehicle so it is covered from day one. You still have to give them the model etc so they know the value.