If they'll be doing this regularly, it'd be better to simply create a new OS user account for them and let them set up their own Zotero profile that doesn't interfere with yours.

If you don't want to do that, they have a few options:

1) Log into their account and add items manually. (I'd strongly discourage this, as it's a waste of time to type in items manually.)

2) Log into their account and use https://www.zotero.org/save to retrieve items. (This is basically equivalent to Add Items by Identifier in the Zotero program. It'll be integrated into a future version of the web library, but for now it's available at this separate URL.)

3) Use https://zbib.org to save items without logging in, use "Link to this version" to save a bibliography, email themselves the link, and then, back on their own computer, view the bibliography and use the "Save to Zotero" button to save the items.

The bookmarklet in combination with a private browser tab would be good method