As soon as you produce an image, written statement (text, tweet, etc.), sound recording, etc. it is immediately protected under copyright law. It's not like a patent for an invention, where you have to file official paperwork. This means that if you're publishing a book, or creating a website, and you want to include someone else's photographs, even if you found them for free on the internet, you probably have to get written permission. Check out some exceptions below:
If you're using images for a presentation in class or to include in a research paper, just to be shown to your teacher and classmates, for a specific assignment, you can use any images you want. You just want to make sure you cite everything correctly, so your professor can check your sources. However, if you then want to present that same PowerPoint to the public at a conference, or submit that paper to be published in a journal, you would have to get permission from the copyright holders for the images you use. However, there are even exceptions to that! Check them out below:
There is a non-profit solution to the hassle of getting copyright permissions. People can now publish images on the web and tell you exactly how you're allowed to use them. So a photographer can publish their images with a Creative Commons license that allows people to use it for free, as long as they attribute it to them and don't change anything. Someone else might publish images for non-commercial use only, but allow you to modify them. People can even require that if you modify their image and create something new, you have to share the result openly with everyone (called ShareAlike). Go to the Creative Commons website for more information about the licenses, with links to searchable databases of creative commons images. To use an image, just copy and paste the Creative Commons license next to the image with an attribution:
Works are only covered under copyright for the life of the author plus 70 years. Works published in the U.S. before 1923, or published before 1963 without being renewed, are now in the Public Domain. This means that they can be used, modified, shared, etc. You don't have to attribute them, or get permission. If you're using them for a school assignment, you should still cite them, so your professor knows where you got them. You can also publish new images with a Creative Commons 0 license (CC0), which effectively enters it into the public domain immediately. For more information about the public domain, visit this Teaching Copyright page.