First step in managing this project would be to place all of the tasks on a large piece of paper, and place them in proper order in priority to get them done. For example, lets say task 8 is dependent on task 5,6,7, and task 6 is dependent on task 1, 3, and task 3 is dependent on task 2. What you would do is assess which tasks you need to get done first. You can follow this sequence of thinking

1) which tasks are dependent on other tasks? Task 8,6,3
2) but there is a second level of dependency, since task 3 is dependent on task 2.
3) Which task should I do first? Task 2.
4) Why task 2? This is the task that I need to complete in order to move on to task 3.
5) Then, I would need to do task 1 in order to move on to task 6.
6) I see task 8 needs 5,6,7. Since I already did the tasks associated with 6 (1 and 3), I can then concentrate on task 6 and 7.

The best way to set it up would be in the form of a decision tree - where you put task 2 on one side, and all of the "branches" or tasks that are dependent on task 2 next to it.

Then, as a project manager, your job is to make sure that these main tasks are done, otherwise the project will stall. If you did them in order of 1,2,3,4... you would not progress at a proper time. It is best to pick and choose the tasks that will help move the project further. If you are under a tight deadline, you want to make sure that all of the prerequisite tasks are completed, so that you don't have to backtrack to complete it. This wastes time.