Activate Kupfer and make sure it is in free-text mode (press period)
Type in a search query and tap Tab to switch to the action pane.
Type "Search With" to find Search the Web's action and tap Tab again to switch to the third pane (indirect object).
Select search engine with the arrow keys and type Return to open the search in a web browser.
The Search the Web plugin uses Firefox' search engines, so you can add Search Engines directly in Firefox and Kupfer will find them later.
You can also install custom search plugins directly, only for Kupfer, in the folder:
~/.local/share/kupfer/searchplugins/
The search engine descriptions must written in OpenSearch format.