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.
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.