How to change all the tables in my database to UTF8 character set?

replace my_database_name with your database name

SELECT CONCAT('ALTER TABLE ', TABLE_NAME, ' CONVERT TO CHARACTER SET utf8 COLLATE utf8_unicode_ci;')
FROM information_schema.TABLES
WHERE TABLE_SCHEMA = 'my_database_name' AND TABLE_TYPE != 'VIEW';

this will build lots of queries which you can run

For single table you can do something like this:

ALTER TABLE tab CONVERT TO CHARACTER SET utf8 COLLATE utf8_unicode_ci;

For the whole database I don't know other method than similar to this:

http://www.commandlinefu.com/commands/view/1575/convert-all-mysql-tables-and-fields-to-utf8