Omni uses a push-pin icon to save items.
To save one item, click the push-pin icon at the top right of the item. This pins it to your favourites.
Click the push-pin at the top right of your screen (beside your name) to see the items you've saved.
Your favourites list opens to show "Saved Records".
To the right of each citation, Cite, Email, Print, Permalink options are are offered. This is also where you "un-save" it.
To save a search, click "Save query", just under the search box.
Click the push-pin at the top right of your screen (beside your name) to see the items you've saved.
Your favourites list opens to show "Saved Records" - click the tab at the top for "Saved Searches".
Your pinned searches are listed with the most recent on top.