See database encoding

mysql> SELECT default_character_set_name FROM information_schema.SCHEMATA 
WHERE schema_name = "database";

See table encoding

mysql> SELECT CCSA.character_set_name FROM information_schema.`TABLES` T,
  information_schema.`COLLATION_CHARACTER_SET_APPLICABILITY` CCSA
WHERE CCSA.collation_name = T.table_collation
  AND T.table_schema = "database"
  AND T.table_name = "table";

See column encoding

mysql> SELECT character_set_name FROM information_schema.`COLUMNS` 
WHERE table_schema = "database"
  AND table_name = "table"
  AND column_name = "column";

See encoding and collation variables

mysql> USE database;
mysql> SHOW variables LIKE 'character_%';
mysql> SHOW VARIABLES LIKE 'collation_%';

Change database encoding

MySQL >= 5.5

mysql> ALTER DATABASE databasename CHARACTER SET utf8mb4 COLLATE utf8mb4_unicode_ci;

Change table encoding

MySQL >= 5.5

mysql> ALTER TABLE tablename CONVERT TO CHARACTER SET utf8mb4 COLLATE utf8mb4_unicode_ci;

Change server encoding

/etc/mysql/mysql.conf.d/mysqld.cnf:
-----------------------------------
...
# Encoding
character-set-server = utf8
_$: systemctl restart mysql.service