There are a few ways that you can manage tasks in SharePoint. You can either use the Out-of-the-Box functionality, which includes the use of lists and workflows, or you can purchase a third-party solution, such as Nintex or K2.
If you choose to use the Out-of-the-Box functionality, you will first need to create a list to store your tasks. To do this, go to the Site Contents page, and click on "Add an app". From there, select the "Custom List" app.
Once you have created your list, you can add items to it, which will represent each task. Each task can have its own set of columns, which you can use to track information such as the task name, description, assigned to, due date, etc.
If you want to automate the process of task management, you can use workflows. Workflows can be used to send out notifications, update task list items, and more. For more information on how to use workflows, see this article: https://support.office.com/en-us/article/Create-a-workflow-with-SharePoint-Designer-2013-8a6bace0-eb83-4fd5-a0a5-2cc5c75f2f8e.
If you are looking for a more robust solution, you can purchase a third-party solution, such as Nintex or K2. These solutions offer a wide range of features and capabilities, such as the ability to create custom forms, add business logic, and more.