Raspbian is a solid distribution for the Raspberry Pi, but it can be a little unintuitive for the more straightforward tasks. For example, the included web browser, Epiphany, doesn't make it easy to change the default search provider from DuckDuckGo. The good news is that it can be switched with a little tinkering.
All the regular avenues of changing the provider: the browser's own settings menu, gconf and about:flags proved dead ends. Eventually, I came across a post by user called "Mequa" on the Raspberry Pi forums that explains the process in detail. I've taken the liberty of replicating the instructions below:
First, you'll need to edit a schema file, which you can do by firing up a terminal and typing:
sudo leafpad /usr/share/glib-2.0/schemas/org.gnome.epiphany.gschema.xml
Then locate this block of XML:
URL SearchSearch string for keywords entered in the URL bar.
<default>'https://duckduckgo.com/?q=%s&t=raspberrypi'</default> is what you need to change. Replace
https://www.google.com.au/#q=%s. It's important to use the local version of Google, otherwise you'll be redirected to the Google home page when you type in search commands, rather than results.
It'd be nice if this was all you had to do, but there are a couple more steps. While still at the terminal, enter:
sudo apt-get install libglib2.0-bin
sudo glib-compile-schemas /usr/share/glib-2.0/schemas
Then all you have to do is restart Epiphany. Of course, you can use any search engine you like, you just have to find the right URL and query string combination to use.
Need Help Changing Epiphany's Default Search Engine [Raspberry Pi forums]