Go to your Google Docs >> open the document >> click Share >> See who has access >> Change >> Let people edit without signing in >> Save & Close >> Share >> Get the link to share >> copy the link >> click Save >> click Done.
Get back to your Google Site >> click Edit page >> Insert >> More gadgets >> Add Gadget by URL >> http://hosting.gmodules.com/ig/gadgets/file/117808631063490062819/url.xml >> Add >> customize Width & Height and insert the link to your spreadsheet >> OK >> Save. (This gadget doesn't work recently so use the method below instead).
Alternative method: Insert >> More gadgets and search for 'iframe'. Insert iframe gadget and configure it with the spreadsheet url.
List view is not available in the new Google Sheets.