Internet Explorer is a web browser (and it's not an integral part of your system).
There are a number of browsers you can use: Firefox, Chrome, EI, Opera, Safari, to name but a few.
Google is a Search Engine. You don't have to use it. Alternatives are Yahoo!, Bing, and Ask, among others.
If Google appears whenever you go online, that's because you have it set as your home page. You can set any website to be your home page, or (as I do) have your browser open to a blank page.