Works that appear on websites are protected by copyright in the same way as works published in other ways. This means that you can only copy a work that is on a website if you have permission from the copyright owner.
The website owner might not be the copyright owner of all works that appear on their site, so you will need to find out who owns copyright in each work that you want to copy. For example, a search engine might show lots of images, but it normally wouldn’t own the copyright in them.
If you are copying the work as part of your homework or for a class assignment, you often won’t need to get permission but if you want to use the work in other ways, such as entering the work into a competition or exhibiting your work publicly (such as on the internet), you will need to get permission from the copyright owner.