You can add a shortcut to your Home Screen to open a specific notebook (see http://feedback.squidnotes.com/knowledgebase/articles/1179331) or to create a new note in a specific notebook (see http://feedback.squidnotes.com/knowledgebase/articles/1179328).
It does not appear to be possible to create a widget that allows for taking handwritten notes directly on the Home Screen (due to the fact that you need to be able to swipe left/right to get to different pages on your Home Screen). Please vote here if you’re interested in a widget that shows a particular note on your Home Screen (and allows you to open it quickly to edit it).utopiate75 commented
looking at the dates this is a long requested feature but nothing as yet (january 2015) so I doubt it will ever happen. shame as the app is superb