If you don't live so far from Estonia, or you want to appreciate the landscape of a road travel, you can come to Estonia by the freshly renovated European roads. :)
Estonia has land borders with Russia and Latvia, so check your route to avoid crossing borders unnecessarily.
European bus travel network, connects 500 cities in Europe. Very good service, you can buy tickets in bus stations or by their website. Prices are not always cheaper than train or plane, but offers discounts for seniors, students, children and groups.
A Latvian bus travel network that connects 145 cities in Europe. With less lines to Estonia, but different time tables, and sometimes cheaper prices.
If you like to drive, Estonia is not far away from you! You can take a ferry from Finland, Germany or Sweden (maybe Norway and Denmark also), and then drive your way in the Baltic countries. If you have a motor-home, or just like to drive in your vacations, its a good idea (specially in summer, because in winter, expect to use winter tires and very slow and slippery roads).
Some friends traveled from Spain to Estonia, in 2 winter days (almost) non-stop driving! Crossing France, sleeping in Germany, crossing Poland, trying (unsuccessfully) to get a shortcut from Belarus (remember that so far Europeans need visa to enter there) and all way up the Baltics to Tartu, the city of good thoughts!
So, do you have a good driving route to Estonia? Let me know in the comments!