beginner: difficulties with timeline

I have entered all my tasks into Project 2000, entered my resources and
allocated them to the tasks. I also set a few predecessors for those tasks
that rely on others to be completed first. What I expected was that Project
would start a new task "as soon as possible" without overallocating
resources. But instead of doing that, all my resources are hopelessly
overallocated. I didn’t change the start-times or end-times, all I changed
was the duration of each task.

Any idea where I’m going wrong?

Thanks for your help.