If the image you have chosen to do a search on is on a Wikimedia Commons page, when you scroll the image down, underneath will be the licensing information. It will either say that it is a Public Domain or one of the Creative Commons licensed image. If you are lucky enough to find a CC0 licensed image, congratulations! But more than likely it will be like the image below.
The license above is for a Creative Commons 4.0 license. Though it is free to use and share, you have to give attribution to the author (creator) of the image in the exact way described in the license. Now if the webpage the image is on is Wikipedia, you will have to search for the image on the page and then click on it to see the licensing agreement, see below image.
This particular image has a license of Creative Commons CC2.0 and it is still free to use but also with stated conditions. And the image below is from Flickr and it too has a CC license, as indicated by the link that says, “Some rights reserved.”
NEXT UP = What the license tells you to doDoes Google sandbox your domain or do owners come after you?