Hello PetMice,
You can use one of two ways to clear out what is in the search/web address bar at the top of Safari. Just tap on the bar then on the right side of it press the round icon with an X in it to clear. Alternatively, when you tap on the bar and it brings up the keyboard you can press the backspace button to clear out the search bar.
So for example say you last searched for "dog" and now you'd like to search for "cat", tap on "dog" up in the search bar then press either the round icon with an X to the right or the backspace button to clear "dog" out of the search bar. You can then type "cat" into the search bar and press Go on the keyboard to search for that item.
If you're talking about completely clearing out the search history, you can do that by navigating to Settings > Safari > Clear History and Website Data.
Clear the history and cookies from Safari on your iPhone, iPad, or iPod touch
Cheers!