When you are in a Google Document, click on Tools in the top toolbar. Then click on Research. Box will open on the right side of the screen. You can research many ways. The 'Everything' category is a general Google search. You can also search Images, Google Scholar, Quotations, use the Dictionary or Tables lets you pull up data in table format.
After you conduct a search in this Research box, you have a few options. Cursor over the result you are interested in and some buttons appear. You can Preview the webpage. That means it opens in a box on your screen. You can insert a Link right into your Google Document (where every your cursor was at). The greatest option here is to Cite your work. Pressing the Cite button will put a citation in MLA format at the bottom of your page as a footer. You can also choose to have the citation in APA or Chicago format.
Along with searching for websites, you can also search for images. Drop down the menu above the search results and you can choose to filter images that are "Free to use, share or modify, even commercially."