To create a new survey in SurveyMonkey, you can copy an existing survey from your account or another user's account, allowing you to use that as a starting point and edit it accordingly. You can make a copy of a survey by clicking "Copy Existing Survey" while creating a new survey, or you can transfer ownership of a survey to another user's account by clicking the three dots next to the survey and selecting "Send a copy" or "Transfer survey". This feature allows you to efficiently reuse existing surveys and share them with others.