In order to register a patent in Estonia you need to file:
an application, (the application form and the list of state fees can be found on the home page of The Patent Office);
the description of the invention in Estonian accompanied by the patent claim, a short summary and drawings.
These documents have to be presented to the Patent Office after having paid the required state fees. After that, the application is processed in the Patent Office, they will publish the application in "Eesti Patendileht" (The Estonian Patent Gazette), and, if no obstructive circumstances occur, after an expert survey the Patent Office will make a decision about granting the patent. This is approximately a three-year-long process.
Following that you have to pay the state fee in order to be listed in the State Register of Patents, and the Patent Office will grant a Patent Letter. The patent is valid for the maximum of twenty years.
The patent is considered valid from the date of filing the application. But you have to pay the annuity fee (which varies from year to year) every year if you want to have a valid patent. You can find information about the state fees on the home page of The Estonian Patent Office.