JOIN to read first table and get possible relationship in the second table Consider a main table as

CREATE TABLE groups
(
group_id int(11) NOT NULL AUTO_INCREMENT,
group_title varchar(255),
PRIMARY KEY(group_id)
) ENGINE=InnoDB


and a second table for relationship as

CREATE TABLE group_members
(
relation_id int(11) NOT NULL AUTO_INCREMENT,
group_id int(11),
user_id int(11),
FOREIGN KEY(group_id) REFERENCES groups(group_id) ON DELETE CASCADE,
FOREIGN KEY(user_id) REFERENCES users(user_id) ON DELETE CASCADE,
PRIMARY KEY(relationsh_id)
) ENGINE=InnoDB


How to get a full list of all groups with an additional column indicating that if a given user is member of each group or not. This means that we will have a WHERE clause indicating the corresponding user_id, and the additional column will show 0 or 1, depending that this user_id has a connection to each group or not.
Based on your updated question:

SELECT group_title, IF(user_id IS NULL, 0, 1)
FROM groups
LEFT JOIN (SELECT user_id, group_id 
          FROM group_members WHERE user_id=1)gMembers USING(group_id)


sqlfiddle