Estonia Phone Numbers, Estonia Phone Code, Estonia Phone Books
Landline phone numbers have 7 digits, mobile (cell) phone numbers can have either 7 or 8. The country calling phone code for Estonia is 372, so all you need is the subscriber number and you’re set.
Free telephone number search
Beware! There are a lot of dubious sites listed in Google which don’t provide direct links, except to casinos!
https://www.telemedia.ee/: People and business search. Use Google Translate.
https://ee.ee/: Estonian telephone directory, for businesses only. In Estonian, English, Finnish, German and Russian. The Google toolbar will translate OK, the English version is the little flag on left below the logo.
https://www.1182.ee/: as recommended by Gigi in the comments is also useful, bit of a Swisss army knife for Estonia really!