When Internet Explorer is installed, it sets up Bing as its default search engine. However, you (the user) can switch the default to any search engine you like, as well as add or remove search engines from Internet Explorer's list of search providers.
Internet Explorer 8 handles search providers a little differently than IE7 and prior versions did - it treats them as add-ons, just like toolbars or other optional browser extensions. (Firefox handles search engines the same way.)
You can access the list of search providers two ways. The first way is by clicking the arrow on the far right of the browser window, past the search bar, and then choosing Manage Search Providers. You can also get to the same place by clicking Manage Add-ons under the Tools menu, and choosing Search Providers from the list of add-on types.
Once you're at the list of search providers, you can do a number of different things. If you have more than one search engine already installed, you can change your default engine by highlighting the one you want to change it to and clicking "Set as default" in the lower right corner. You can also sort the search engines any way you like, or have Internet Explorer sort them alphabetically.
If there is a search engine on the list that you don't want, just highlight it and click Remove. You can always add it back later if you change your mind. If you want to use a search engine but you don't want it to make suggestions for you, click "Disable suggestions" toward the middle of the window. (It's hidden between lines of text, but it appears in blue.)
There is a feature of IE8 which helps to fight adware infections by preventing other applications from changing your default search engine. To enable this feature, put a check in the box on the lower left side of the screen next to where it says "Prevent programs..."
To add another search engine to your list of search providers, click "Find more search providers" in the lower left corner. A new IE window will open up, taking you to the IE Add-ons Gallery where you can look through the three pages of search providers. To add any one to your default list, just click the button labeled "Add to Internet Explorer."