WARNING: THIS PROCESS IS IRREVERSIBLE
Make sure you're deleting the correct league. By deleting a league, any schedules under it will also be deleted. This is IRREVERSIBLE! If there's any chance of deleting the wrong league because of similar or same names etc. STOP and take any necessary precautions such as renaming leagues so you can be sure. The safest option might just be to live with a little clutter.
On your dashboard, click New Schedule and then New League (PRO) or New Tournament:
On the next screen, you'll see a delete button next to each league:
you can't delete leagues with published schedules. you need to make those schedules private first by going to their schedule maker page and clicking the make private button at the bottom right.
To make sure you know which league you're deleting, it will make you type the league's name: