Hitching a ride is fairly common practice in Estonia. Students on a weekend visit home from college and even kids hitchhike. But as always with hitchhiking, there are risks, so think twice before setting off to do it on your own. To get to Pärnu from Tallinn, take bus N°14 or 18 from the Viru Centre Bus Terminal all the way to the end of the line (Laagri), and join the queue.
To get back to Tallinn, head out of the centre of Pärnu on Tallinna mnt., and to get to Riga, Riia mnt.