By your own car you can come to Estonia by Via Baltica from South Europe, through Latvia and Lithuania. Or if you prefer to come by car on a ship, you can come from Finland, Sweden, Russia and Germany. Wherever you're coming from and heading to you'll need your car's registration papers and a valid insurance policy, such as the international green card. But remember that in Tallinn's Old Town is hard to move by car, it is not even allowed everywhere. Domestic road network is dense and covers all regions of the country.
Car rental in Estonia is very cheap compared to Western Europe. You can get a car shared between two people for 150EEK/person/day.