Once your organization has enabled Linked Tasks under "Add-Ons" you can manually link tasks on the dashboard, or link them via API.
To link a task via the dashboard, simply hold the option key (alt key if you are using Windows), select a task, and then hover your selection over the task that you wish to designate as a prerequisite - the task will have a blue outline on it.
After you release the mouse, the tasks will be linked together, and their sidebar icons will update to indicate the link and direction of the dependency structure.