How to determine the default characterset and collation of a MySQL database?

First use the "mysql" command on a linux box to connect to the server and set the default database:
mysql -p -u username -h mysql_server_hostname database_name

Upon successful connection use the "show variables" mysql command to query the default character set and collation:
show variables like '%database';

You'll get something like this:
+------------------------+-----------------+
| Variable_name          | Value           |
+------------------------+-----------------+
| character_set_database | utf8            |
| collation_database     | utf8_general_ci |
| skip_show_database     | OFF             |
+------------------------+-----------------+
3 rows in set (0.00 sec)

To change the default characterset of a database use the following command:
ALTER DATABASE your_database DEFAULT CHARACTER SET utf8 COLLATE utf8_general_ci;