You can use the ALTER TABLE/DATABASE SQL statements to convert your data.
To set the default character set for a database, use the following statement.
ALTER DATABASE <database_name> CHARACTER SET utf8;
This does not affect any existing tables, but any future tables created in this database will use utf8 by default.
For each table you want to convert to utf8, use the following statement.
ALTER TABLE <table_name> CONVERT TO CHARACTER SET utf8;
This will automatically convert all text columns to utf8.