Specify the utf8mb4 character set on all tables and text columns in your database. This makes MySQL physically store and retrieve values encoded natively in UTF-8. Note that MySQL will implicitly use utf8mb4 encoding if a utf8mb4_* collation is specified (without any explicit character set).
In older versions of MySQL (< 5.5.3), you'll unfortunately be forced to use simply utf8, which only supports a subset of Unicode characters. I wish I were kidding.