It’s the blue and white icon in the top right hand corner. Clicking it enables you to edit published or locked objects. But, remember to click it again once you have finished editing changing it from red to blue again.
The ‘Design Mode’ is also only a feature available in the Professional version of the ActivInspire software.
You can click on Help>About within ActivInspire to find out if you are using the personal or professional edition.
If you have an ActivBoard or other Promethean hardware please look at article 10937 on http://www.PrometheanKB.com if you need to upgrade to the professional version.