After you create your group you'll be able to administer it from your group's manage page.
From your manage page you can participate in the private group discussion, just like group organizers. And you can leave the group in the same way, by clicking on the "Click to leave this group" link at the bottom of the right sidebar on your participate page, and then confirming your decision.
After you leave the group you will no longer be able to access your manage page or get notices about group discussion. You will have to re-apply if you want to join again, and be re-approved by group administrators. All actions you created that are sponsored by the group will remain as they are -- you will still have access to them, but so will group administrators.
The first time you visit a group as an administrator, you will have the option of choosing the group as your Action Network default group, the page you see after you log in. You can always change this setting by editing your profile or hovering over the icon in the upper right and clicking Edit under the Default Group section. This will also set this group as the default sponsor for any new actions you create.