You can use DESCRIBE:
DESCRIBE my_table;
Or in newer versions you can use INFORMATION_SCHEMA:
SELECT COLUMN_NAME
FROM INFORMATION_SCHEMA.COLUMNS
WHERE TABLE_SCHEMA = 'my_database' AND TABLE_NAME = 'my_table';
Or you can use SHOW COLUMNS:
SHOW COLUMNS FROM my_table;
Or to get column names with comma in a line:
SELECT group_concat(COLUMN_NAME)
FROM INFORMATION_SCHEMA.COLUMNS
WHERE TABLE_SCHEMA = 'my_database' AND TABLE_NAME = 'my_table';