This is an interesting and controversial area of the law. Google images allows users to view and download copies of images. Google does not own copyrights in these images, nor does it obtain permission to use or license them. Rather, copyrights in these images are owned by the photographers and/or the people or companies to whom the photographers licensed or sold the photographs. If you use any such images in your video, you might be deemed to violate the copyrights owned by the photographer (or his licensees or assignees). Further, you might be deemed to violate rights of publicity owned by persons who appear in these videos, and/or trademarks that appear in the images. While the doctrine of fair use could potentially give you some degree of protection, it is a misunderstood and quite limited doctrine. Even if your video is for academic, journalistic or educational purposes, if it has a commercial component (i.e., you are trying to make money from posting, licensing or otherwise showing it), the doctrine of fair use probably will not protect you. Thus, your best bet is to obtain permission from the owners of the copyrights in the photos.
Obtaining permission might not be so easy---first, the copyright owners have no obligation to cooperate with you. Second, it may not be easy to identify the copyright owner. Many images that appear in Google Images do not identify the name of the photographer and/or copyright owner. Third, even if you can identify the copyright owner, he or she might want to charge you a significant amount of money to use the photograph.
This leads to the key point---it is really not such a good idea to rely on Google Images to obtain photographs for use in your project. Why not try to obtain the images from legitmate photostock companies, such as Getty Images, who will issue licenses that permit you to use the photographs? This would be a much safer approach, and you will reduce dramatically the likelihood that you will face an expensive law suit.
One further point---if you are making a video, chances are that you will face several IP questions. You really should find an IP lawyer to work with you on such matters. If you retain an IP lawyer, you will end up saving a lot of money in the long run.
Are you doing this for fun or profit? If you are not charging a fee for it, you have a good argument that this constitutes fair use of the images. If not, someone will issue a take down notice. If not, likely the first step that they would take would be to ask you to take it down, so the penalty would not be that great.
It might not hurt to ask for permission. Sometimes the copyright owners may negotiate a license.
[In accordance with the Avvo community guidelines, this communication does not constitute "legal advice", nor does it form an attorney-client relationship.]
It is a little unclear exactly what you are asking. If what you are asking is whether you are free to use any images that result from a "Google images" search online without permission, then the answer is no. Those images are almost certainly all copyrighted and you would get in trouble.
When you do a Google images search, Google only displays a cached thumbnail of the image itself (usually). Storing a cached thumbnail alone was found to be acceptable fair use. But if you click on that thumbnail, you are taken to the actual image itself which is not stored on Google's servers. You would definitely need permission to copy that image and post it anywhere else online.
Linking to the image should be ok.