I could not believe that changing default Search Provider in Internet Explorer 10, probably in couple of versions below too, was complicated, but it surely is, of course, if you are located outside of United States.
I have clicked on the Tools icon in Internet Explorer 10 and selected ‘Manage Add-ons’. In the left pane I have choosed ‘Search Providers’ ad since only Search provider was ‘Bing’ I have clicked on the link ‘Find more search providers’ in the bottom of the ‘Manage Add-ons’ window.
I was redirected to the Internet Explorer Gallery in my native/local language where I have browsed all of the listed Add-ons and also used the Search box trying to find the ‘Google Search Provider Add-on’ but without luck.
It was not listed at all. So I had to change the language in use using the link that even is not linkable but grey instead as seen in the picture:
Once I have changed language/location to United States (English) I have selected Add-ons and Google Search was listed at the top for Search Providers field.
Click on it and choose it to set it as your default search provider in Internet Explorer.
I have also noticed that I was not able to set it as the default provider in the box above and therfore I have removed Bing from available Search Providers.