You can create tasks from different task lists. The first one is the most obvious: your personal task list.

Go to My Tasks > To-do and start typing in the task creation text field. Hit Enter on your keyboard to create the task. The task created will be unshared by default. You can then click on the newly created task to edit the task information in the task card.

You can also insert a task anywhere in the list. Hover your cursor between two tasks and click on the little + icon at the left of the line separating two tasks, then click on insert task. Type your task label and hit Enter to create it.
  

You can create tasks from two subject task lists: To-do and All tasks the same way as described above, except that you can pre-assign the task:

Whether it is in the task create text field or from the in-line task creation, you can select the assignee by clicking on the avatar (your by default) on the left of the text field. You can then select the assignee for the task(s) you are about to create. You can also create unassigned tasks this way.

All tasks create from within a subject will be shared on this subject by default.

 
Create tasks from team member profile task lists
You can create tasks directly from your team members profile task lists. Click on a team member's name or avatar to access their profile, the click on the task tab to show their task lists.

You can then create tasks as you would for yourself. The tasks created will be assigned to the team member on who's profile you are on.