Fonts that are not restricted agains embedding are automatically embedded in the PDF when you export from ID. If you've used a restricted font you'll get a warning, and you can either replace it or check with the printer to see if it's a common system font that they also have.
There is nothing illegal about embedding fonts with the correct permissions, and this is the preferred method as the fonts are not available outside the PDF.
InDesign, by default, embeds all fonts which have the right to be embedded when you create a PDF file. You can set up a Preflight profile on the Preflight panel to look for fonts which don't have embedding rights.