There are two different task types to create:
These tasks are only for you. Accessible at any time from the Tasks page. No one else can view/edit these tasks.
These are any task created inside a project and inherit the group, board, and project's permissions. All tasks are public by default. See how to make project tasks private here.
1) Create individual task
Navigate to Tasks.
Click on Create a task and enter your task name and other details. See how to create a task from a template here.
Click Create task.
2) Create project task
Navigate to Projects and open/create a project.
Go to a Task group header, click Create task and enter your task details. See how to create a task from a template here.
Click Create task at the bottom.