There are several ways of searching the Internet on the Internet Browser of your Nintendo 3DS.

One option is to use the search field of the Menu. You can add text here, and after tapping Search, it will use the search engine you selected to perform a search. You can change your prefered search engine by tapping on the wrench icon in the Menu.

Alternatively, you can select a piece of text on a website and directly search for that. You hold down your stylus at the start of the text you want to search for, and as soon as the cursor appears, you slide to select the text. Then tap on Search at the bottom right. The search window will open with the selected text already entered. Tap Search once more to start searching.