You can use CREATE TYPE to declare your enum:
CREATE TYPE tfoo AS ENUM('foo','bar','dummy');
And use an array of it to store the values:
CREATE TABLE foo (foo_id serial, foo_enum tfoo[]);
To insert:
INSERT INTO foo(foo_enum) VALUES('{foo,bar}');
Or
INSERT INTO foo(foo_enum) VALUES(ARRAY['foo','bar']::tfoo[]);
Another approach would be using another table to store the enums and a foreign key to the foo table. Example:
CREATE TABLE foo (foo_id serial primary key);
CREATE TABLE foo_enums (foo_id integer references foo(foo_id), value tfoo);
And them insert the multiple values into foo_enums:
INSERT INTO foo(foo_id) VALUES(nextval('foo_id_seq'));
INSERT INTO foo_enums(foo_id, value) VALUES
(currval('foo_id_seq'), 'foo'),
(currval('foo_id_seq'), 'bar');
'nor that stupid backtick from MySQL.'foo'is not a table name. It's string literal (even with MySQL).