If you want to come to Estonia by plane, Tallinn has an airport (called Tallinna Lennujaam) very close to the city center (4km), with very fast connections by city bus or taxis to the city center! If it's your first time, it might be the best choice. Plus, the airport has free wireless internet! :)
- Estonian Air
The National Airlines flies from Tallinn to many European capitals and cities.
In the website (in Estonian, English and Russian) you can book and pay with local bank cards or international credit cards. Prices are good if you book in advance, and you can have a interesting taste of Estonia, with blond flight attendants, surrounded by Estonian language.
A British low cost Airline that connects Tallinn with daily flights to London (£19.99) and Berlin (€19.99).
It's cheap, but with some gotchas: Hand luggage price not included (cost by piece); Extra luggage (more than 20kg) is veeery expensive (cost by extra kilo, watch out!); Payment adds extra costs (if you can, pay with visa debit cards, it's cheaper).
The website, and the whole service, is done in almost all European languages, and don't be surprised if you find a flight attendant that speaks your language.
There are more airlines working in Tallinn, like the Finnish Finnair, Latvian Air Baltic, Dutch KLM and German Lufthansa, but it all depends where you are coming from, and what you want. If you are looking for the cheapest way, I recommend getting to Europe first (London, Berlin, or other European capital), and then with one or two flights you are in Tallinn.