You can edit a task in two ways
The fastest way to edit a task is directly in the task list. You can do this by simpley placing your cursor on the task that you would like to edit. Once your cursor is in the task, you can just start typing. When you're done, your changes will be automatically saved.
You can assign the task to someone new by clicking the name of the person currently assigned to the task.
If you're on the task details page, you can edit a task by clicking the 'Edit Task' button.