HOW! Too big and complex of an answer for a posting.
PERT, CPM and GANTT are ALL used within a project for different purposes / outputs.
However as a planning tool and to "control" a project GANTT is easiest to communicate to team members and responsible parties (for their responsibilities).
CPM (Critical Path Management) is a good tool to identify which among many ongoing activities are the ones that (at this point in time) constrain and determine how fast progress can occur.
PERT shows critical timing information and activity flow in a tight (tighter than GANTT) pictograph.
Summary - depends on your audience and your purpose. You probable can use all of them to your benefit on many projects.