The first thing to know is that you have to physically be there to apply. I went to Estonia and applied at the local police station. I know that sounds weird but thats how you do it. In Estonia, this is where you go to renew driver's licenses and a lot of governmental things.
It was relatively painless. I didn't need to make an appointment. It's just like a DMV. You take a ticket and wait. The woman behind the counter asks some questions, for your passport, biometrics (photo and finger prints) and 50 euros. You then you wait to hear a response within two weeks.
An annoying part is that you have to show up again in two weeks to pick it up in person. Mine is still waiting for me in Estonia as I've not been back yet and I can't have a friend pick it up for me (it has to be me!).
Be prepared to spend two weeks in Tallinn, therefore, which isn't bad as the prices are quite reasonable and the food is good.