There are three options for embedding Google spreadsheets into a Google Site from the Site editor. They all start the same way:
Insert > Drive > Spreadsheet ...
Select the spreadsheet to embed
Then choose one of the following options:
- View as Spreadsheet
- View as Spreadsheet (published)
- View as List
You can also embed a spreadsheet in an iFrame so that it is editable by those with edit access. See iFrame example - Editable Google Spreadsheet