I haven't tested any of this with a survey list, but with custom lists these techniques work.
List forms can be redirected after submission by adding a Source parameter to the URL. So if you are linking to the survey from somewhere (and not having users click the "New" button on the survey's overview page), modify the link to be something
like this: <a href="http://yoursite/lists/yoursurvey/newform.aspx?Source=http://yoursite/pages/thank-you.aspx">Respond
the Survey</a> where "thank-you.aspx" is your custom thank you page.
Or you can create a new view of the survey using the web UI (no need for SharePoint Designer) and add a content editor web part at the top of the view with your thank you message.
part on the survey overview page.
Or you can do the same using a data view web part instead of SPServices if you prefer server-side code.