When someone assigns you a project task, you receive a mail message in your Incoming Mail with a subject "Project Task Assignment". When you read the message, OfficeTalk informs you that the assigned task has been added to your personal task list.
If you are assigned a parent project task which has a number of sub tasks then each of these sub tasks will appear in your task list under the parent task keeping the original structure.
Once the assigned task is in your personal task list, you may treat it in just the same way as any other task. For instance, you may schedule it into your diary, change its priority, mark it as completed, add notes to it or even delegate it to another user. If you mark the task as completed or set it's percentage complete property then OfficeTalk will update the associated project with this information.