To run a checklist, first, you must create a template from which it inherits its base content.
After you have your template set up you can create a checklist based on your template in a couple of ways...
If you're on the dashboard you can click the 'Create & Run New Checklist' button. If you're not on the dashboard, click on the 'Quick Create' button (green button with + icon) from the left toolbar, and then click the 'New Checklist' option.
Both methods will open a popup. Select the template you are basing the checklist off and then give your checklist a name. Click the 'Create & Run New Checklist' button. Your checklist will be created and you will be immediately redirected to it.