Obtaining Estonian citizenship
In general, citizenship could be obtained (also called naturalization) or re-instated if lost as a child.
Conditions for applying for Estonian citizenship:
you have a long-term residence permit or the right of permanent residence
you have lived in Estonia, prior submitting an application, for at least eight years on the ground of a residence permit or by right of residence, of which at least the last five years on a permanent basis
you have passed the Estonian language proficiency examination (this exam is not required, if you have acquired the basic, secondary or higher education in the Estonian language)
you have passed the examination of knowledge of the Constitution of the Republic of Estonia and the Citizenship Act
you have a permanent legal income
your place of residence has been registered in the population register of Estonia
you are loyal to the Estonian state
Conditions for re-instating Estonian citizenship:
you have lost citizenship as a minor;
you are permanently living in Estonia on the ground of a residence permit or a right of residence;
you have been released from your previous citizenship or will be released from it because of the resumption of Estonian citizenship.
The condition and process of releasing from previous citizenship is not something that every country demands (some accept multiple citizenships).
When applying for re-instating the citizenship you should apply for a specific certificate and the Estonian Police would issue a certificate stating that a person will receive Estonian citizenship once released from the previous citizenship. This has to be taken to the embassy of the current citizenship country. Once the Estonian citizenship has been conditionally granted the corresponding decision has to be again taken to the embassy and the person should apply for and receive a certificate proving he or she has been released from the previous citizenship.
In practice people tend to want to keep many citizenships as they see benefits and value in that but in case of Estonia only one citizenship is allowed.