Let's say you want to look at a particular issue, and you want to exclude Brookings from your search because you are already familiar with their results. Here is how you do this: add -Brookings.edu to your search terms.
Click to enlarge.
To exclude the site of the institution, enter the full web address as illustrated above. If you exclude "-Brookings" without the ".edu" all pages that contain the word Brookings will be excluded. You may thus not get reports that refer to Brookings, for example in the footnotes.
Do you have further questions about search? Let us know in the comments below.