Usually, you create all the indexes you need when you are creating tables. Any column declared as PRIMARY KEY, KEY, UNIQUE, or INDEX will be indexed.
Sometimes you will find that you are running many queries based on an unindexed column, and in this situation, you can add an index using the CREATE INDEX statement.
Interestingly enough, the CREATE INDEX statement is mapped to an ALTER TABLE statement before being executed. The ALTER TABLE statement can be used for this and many other purposes.