Basically, once Mikhail Gorbachev came to power, and proclaimed a new era of free speech, the Estonians decided to test it by singing (frequently a highly patriotic song called "Land of My Fathers, Land That I Love") every time they wanted to protest something. It proved an effective tactic, with no violent repercussions.
They came to realize that as long as the Estonians didn't shed any blood, Gorbachev couldn't justify sending in tanks to quash demonstrations. So they developed a highly conscious tactic of non-violence, and in the end, achieved Estonian independence.
There's now a documentary film about it called The Singing Revolution. Here's the trailer. Be inspired.