Have the editor _package_ the file so it includes fonts (with a few exceptions). Look at the font list and remove any duplicate fonts you have installed on your computer (move them to a non-system folder for now). InDesign will use the fonts included in the "Document fonts" folder in the package. (You can install those fonts if you are doing the editing on a continual basis.)
If the editor is on a Mac and used Mac-only fonts, you need to discuss font usage. For example, Helvetica is not included with Windows, but comes on Mac--plus, it is not a cross-platform font. If that font is required by the designer, then all editors would need to swtich to an OpenType version of the font; it would have a slightly different name: Helvetica Std. This would be a one-time change--after that, all the computers would use the newer font.
Of course, one would switch the font to another similar font.
Also, have your editor open the document(s) and check the Merge User Dictionary in Document preference. That way, any additons they made to their user dictionary will travel with the document.
[Edit] Added from another post to make this answer as complete as possible:
Just a note about Microsoft fonts. The Mac versions of Microsoft fonts (Ariel, Times New Roman, Windings, etc.) are not always the same as the Windows versions. Better to uninstall the Mac versions and (re)install Windows versions on the Macs.