How can I add comments in MySQL?

You can use single-line comments:

-- this is a comment
# this is also a comment

Or a multiline comment:

/*
   multiline
   comment
*/

"A comment for a column can be specified with the COMMENT option. The comment is displayed by the SHOW CREATE TABLE and SHOW FULL COLUMNS statements. This option is operational as of MySQL 4.1. (It is allowed but ignored in earlier versions.)"

As an example

--
-- Table structure for table 'accesslog'
--

CREATE TABLE accesslog (
aid int(10) NOT NULL auto_increment COMMENT 'unique ID for each access entry', 
title varchar(255) default NULL COMMENT 'the title of the page being accessed',
path varchar(255) default NULL COMMENT 'the local path of teh page being accessed',
....
) TYPE=MyISAM;

From here you can use:

#  For single line comments
-- Also for single line, must be followed by space/control character
/*
    C-style multiline comment
*/

Several ways:

# Comment
-- Comment
/* Comment */

Remember to put the space after --.

See the documentation.