NationBuilder has a built-in survey page. If you build your survey using this page type, responses will be recorded in your people database and you'll be able to tag people based on the answers to your survey questions. This is usually the best way to survey your supporters.

The SurveyMonkey help center includes information about embedding their surveys into a website. You could place the code generated on a basic page on your website.

Please note: to add any code to a page on your website, you'll need to go the page's template, rather than the content editor.