When adding a task, you will be presented with the Task Information window. This is the same window you will see when editing a task, and the steps are the same.
Once you press OK however, instead of immediately sending your suggestions to the manager, you are presented with the "move new task to final position" window:
The new task (with an ID of 0, because it is not yet inserted in the Project) is shown in the position you clicked. In this case, the user right-clicked on task 28, and selected Add New Task. LiveProject by default inserts the new task right below the one you clicked on. If no task is highlighted, the new task will go to the end of the project.
As seen on the picture above, the mouse-cursor will change, indicating this task can be moved. Simply click, and drag it to the position you would like to insert it at. Indentation will occur automatically. When you have placed the task at the right location, press the Submit button to send it to your project manager. If you need to make more changes to the task, press Cancel to return to the Task editing window.
You can also indent a new task to make it a child task of an existing task as shown in the picture below.