If you set up successor/predecessor links between the tasks then changing the start or finish date of the first task will cause the other bars to move.
Of course you need to be careful that the tasks have the appropriate constraint types and constraint dates. You also need to remember that resource calendars (i.e. resource availability) and task calendars may also have an impact. Finally, you need to concern yourself with whether the project was scheduled from the start date or the finish date.
Quite simple, really.