Añadir nuevo campo

Creo recordar que:
ALTER TABLE tabla ADD campo TIPO_DE_DATOS;
Seguro que en el manual de MySQL encontrarás la sintaxis correcta.

Ok para hacerlo debes ejecutar la siguiente consulta:
ALTER TABLE tabla ADD nuevo_campo VARCHAR( 10 ) NOT NULL ;

Eso lo puedes hacer con
Alter table ...
Ejemplo añadir un campo TIMESTAMP de nombre Fehca a la Empleados
ALTER TABLE Empleados ADD Fecha TIMESTAMP;
Espero te sea de ayuda.
Sintaxis de ALTER TABLE
ALTER [IGNORE] TABLE tbl_name
alter_specification [, alter_specification] ...
alter_specification:
ADD [COLUMN] column_definition [FIRST | AFTER col_name ]
| ADD [COLUMN] (column_definition,...)
| ADD INDEX [index_name] [index_type] (index_col_name,...)
| ADD [CONSTRAINT [symbol]]
PRIMARY KEY [index_type] (index_col_name,...)
| ADD [CONSTRAINT [symbol]]
UNIQUE [INDEX] [index_name] [index_type] (index_col_name,...)
| ADD [FULLTEXT|SPATIAL] [INDEX] [index_name] (index_col_name,...)
| ADD [CONSTRAINT [symbol]]
FOREIGN KEY [index_name] (index_col_name,...)
[reference_definition]
| ALTER [COLUMN] col_name {SET DEFAULT literal | DROP DEFAULT}
| CHANGE [COLUMN] old_col_name column_definition
[FIRST|AFTER col_name]
| MODIFY [COLUMN] column_definition [FIRST | AFTER col_name]
| DROP [COLUMN] col_name
| DROP PRIMARY KEY
| DROP INDEX index_name
| DROP FOREIGN KEY fk_symbol
| DISABLE KEYS
| ENABLE KEYS
| RENAME [TO] new_tbl_name
| ORDER BY col_name
| CONVERT TO CHARACTER SET charset_name [COLLATE collation_name]
| [DEFAULT] CHARACTER SET charset_name [COLLATE collation_name]
| DISCARD TABLESPACE
| IMPORT TABLESPACE
| table_options