If the character set of your data is Unicode (UTF8) you can use the following command to export it using this charset:
mysqldump -uUSERNAME -pPASSWORD --default-character-set=utf8 USER_DATABASE > backup.sql
Replace USERNAME, PASSWORD and USER_DATABASE with the appropriate values for your database and you will have a file named "backup.sql" properly encoded in UTF-8.
When you import backup into an empty MySQL database, you can set the exact character set for the data that will be inserted. To do this, use the following command:
mysql -uUSERNAME -pPASSWORD --default-character-set=utf8 USER_DATABASE < backup.sql
Replace --default-character-set=utf8 with the charset used for the creation of the backup.sql file. This will ensure that your data is inserted correctly.