Trellis has a built-in search option for the header. To enable this you can go to Appearance → Mediavine Trellis → Display and then activate the Enable Search Bar setting.
Click Save in the upper right corner of the Mediavine Trellis settings to save the search bar setting, then view a post to see the search bar added to your header.
If the search bar is not added to your header, clear the Page CSS from the Manage Trellis JS/CSS options in the admin bar, and clear any other caching plugins you might be using.
You can also add search widgets to the sidebar or footer area by going to Appearance → Widgets and dragging a search widget into the Primary Sidebar or any of the three Footer Widget areas.