Windows Phone uses Internet Explorer as it is default web browser and Bing search comes integrated with it. The service may vary depending on your country, for instance, the Bing search integrated with Yandex in Russia.

If your Lumia is running on Windows Phone 8, it allows you to choose your default search provider, to do that go to Settings, then swipe left to Applications > Internet Explorer > advanced settings, and change the Default search provider.

As an optional search engine, you can download the Google search app from the Store (formerly known as Marketplace) and pin it to your start screen.