A detailed construction of a non-finitely generated version can be found at http://math.stackexchange.com/questions/88980/infinite-group-with-only-two-conjugacy-classes as pointed out in the comments.

A detailed construction of a non-finitely generated version can be found at https://math.stackexchange.com/questions/88980/infinite-group-with-only-two-conjugacy-classes as pointed out in the comments.