An Introduction - basic words you'll need during the first weeks 

One way to see Estonians smile during your stay here is saying them something in their own language. Estonians are modest and think that their language is too small for someone foreign to bother to learn something. If you know even some small basics like Aitäh, Tere and such can light up someone’s day. 

So here are the basics for you:

Tere - Hello!
Head aega! - Goodbye
Tšau! - it’s like Aloha, you can use it as hello or goodbye
Kuidas sul läheb? - How are you doing? (but most Estonians don’t like the question)
Hästi - I’m doing great! (we keep it one sentence...we don’t like words)
Palun - please; you're welcome 
Aitäh - thanks

Estonians in general don’t like small talk. They do like complaining about things such as the weather, government and loud people next to them. We as a nation are basically the Ron Swanson. Be patient with us and don’t give up before you get to know us, we’re actually really nice under the layer of a bitchy face.

Mis sinu nimi on? - What is your name?
Minu nimi on… - My name is… [and then you say your name]
Meeldiv kohtuda! - Nice to meet you!
Kust sa pärit oled? - Where are you from?
Ma olen pärit... - I'm from...(sometimes country will end with the case ending of “-lt” or “-st”, example when you are from Germany you’d say “Ma olen pärit Saksamaalt” but if you are from Finland it would be “Ma olen pärit Soomest”.)
Ma ei räägi eesti keelt! - I don’t speak Estonian!


Tere hommikust! Good morning!
Tere õhtust! - Good evening 
Head ööd! - Goodnight
Head aega! - Goodbye 
Terviseks - Cheers! (you also say it when someone sneezes) 

And finally some actually useful phrases

Kus on lähim Prisma? - Where is the nearest Prisma? (that’s the cheapest shop in Estonia to buy your macaroni from, you’ll need it, trust me)
Kus on lähim Selver? - Where is the nearest Selver? (that’s one of the most expensive’ll go there if you want to impress someone) 
Kus on päike? - Where is the sun? (a question you’ll be asking yourself all the time when you are in Estonia)