It's not a good idea to log in as root; a small typo can result in a big loss of data. Better to log in as a regular user and switch to root only when necessary.
I want to edit a shell shript file which name is mydate. But How can I run this shell shript file. Someone told me to use "chomd +x mydate", but what meaning it is and where I should use!
Did you try "man chmod"? The explanation is there.
By running "chomd +x mydate" you are adding execute permission for everybody to the file called "mydate". Execute permission on a file means you can run it as a program.
Paul.