Then you’ll want to examine permissions and make the appropriate changes.
See
http://codex.wordpress.org/Changing_File_Permissions
Also, make sure you don’t have any caching plugins running while editing templates.
I too am having trouble with this.
I want to change the font color and size in my header. So I edit blog-description color and blog-name color in style.css using the theme editor ( tiga theme )
I changed the color and font-size, update says sucessful but no changes are visible when site is viewed.
I also edited the style.css externally with a text editor and reloaded it via ftp.
I have no plugins running
I have refreshed browser many times.
I tried it on another PC that has never been to this site..
Am I editing the wrong file (style.css)?