Estonia's train network does not cover the whole country. The quality of services has suffered considerably from privatisation and the main means of local transport is now the bus. Tallinn has three frequently-going local train lines Tallinn-Keila-Paldiski/Riisipere and Tallinn-Aegviidu see: (http://elron.ee).
The Tartu-Tallinn train route is good, fast and offers wireless internet access.
Domestic routes are operated by Elron (http://www.elron.ee).
The international bicycle project BaltiCCycle (http://www.balticcycle.eu) may provide you with a lot of information and help.
The road system is quite extensive although road quality varies. The speed limit in the countryside is 90 km/h and 50 km/h in the cities unless specified otherwise. Passengers are expected to wear seat belts. Lights must always be switched on.
In the central areas of bigger cities, a fee is levied on parking cars, but finding a provider of tickets is sometimes difficult as mobile parking is widespread.
Estonia has lots of car rental companies and the level of English spoken by their representatives is generally very high. If you go to Level 0 of Tallinn international airport, there are several car rental agency counters.
Car rental in Estonia is very cheap compared to Western Europe. You can get a decent car shared between two people for approximately €10/person/day e.g. a 2004 Fiat Punto.
An excellent day trip is to drive from Tallinn to Tartu. It takes about 2.5 hours each direction.
As of September 3, 2006, the drive from Tallinn to Tartu has been much improved. Outside of Tallinn, it is a two lane paved road with some construction ongoing to upgrade it. It takes two to two and a half hours. There are few sights of interest along the way. The terrain is flat and most of the road is bracketed by a birch tree and a few pines. Sam's Grill about 1/2 way between Tallinn and Tartuis recommended as a place to stop. There is a gas station next door.
Driving in Estonia can be more dangerous than in much of Europe and the United States.Some drivers can be aggressive, recklessly overtaking vehicles and traveling at high speed, even in crowed urban areas. Estonian laws against driving under the influence of alcohol are strict and follow a policy of zero tolerance. Unfortunately, accidents involving intoxicated drivers are distressingly frequent.You should always remain alert to the possibility of drunk drivers and drunken pedestrians. Standards of driving can range from bad to downright lethal. The best advice is to drive defensively: don’t assume your fellow drivers will do what you expect them to do, like avoiding overtaking in poor visibility or signal before they merge into your lane. If you can avoid it, it’s probably best not to drive on inter-city highways.
Estonia has a comprehensive bus network all over the country. All bigger cities like Tartu, Pärnu, Viljandi and Narva are accessible by bus. There is a journey planner called peatus.ee, in Estonian, English and Russian. There is also a timetable search at t-pilet.ee. But also check (http://www.eurolines.ee) only between bigger cities and to outside Estonia.