To be honest, I am not completely sure if an application as old as yEd is able to support tamil script.
However, if it does, you need to choose a font that can display tamil glyphs and be able to type the appropriate character codes.
To choose a different font, select a node or a label, go to the properties view in yEd's lower right corner, click into the "Font Family" field, and choose the desired font.
Unfortunately, I cannot tell you how to type the appropriate character codes - I simply do not know.