In order to answer this question, it’s safer to always assume: Not unless specifically stated otherwise, you cannot just go and grab images from Google Images or Flickr without the owner’s permission. Now exceptions to the rule are usually given in the form of copyright notices. But what do they mean?
When artwork is copyrighted you simply cannot use it. You will usually find this information on the page near the image, in the footer, or on a separate page with legal information. The photographer will not allow you to use this artwork for free for your personal or creative projects. In a situation like this always contact the person and ask for a quote. When using copyrighted artwork, you should have it noted on your website:
The public domain is a fairly complex subject, when it comes to intellectual property there are many rules to follow. To sum it up in a few sentences it means something has been copyrighted in the past, but because it has been 70 years after the author’s passing, the works become free to use for the general public. Photography that falls under public domain is officially announced, and can best be found via official resources where the license is clearly stated.
Did you find a cool vintage photo on the web, and the source is unknown? Try and find its original source with a reverse image search like TinEye.
Photographers can freely announce that their artwork falls under the Creative Commons license. This license has been introduced to encourage and share creative work, and allow others to be creative on their part, based on the work of others.
There are 6 different types of Creative Commons licenses, and just because something has a Creative Commons license does not automatically mean you can use it for your commercial project. For example, this way photographers can let you know that they allow you to (re)use the work as you please, but not sell it or use it in any way commercially.
When there are no license options shown, it’s always best to play it safe and get image artwork from a trusted source. For example a website selling stock photography. Or a professional photographer to shoot the images needed for your project.
You infringe upon someone the intellectual property rights of someone else by using the author’s copyrighted work without his permission. This may seem obvious but you are responsible for the consequences. When you using copyrighted work in a commercial project you may need to pay damages, and discontinue from further using the material without permission.
A worst case scenario would involve being ordered to immediately destroy the works, and/or give the owner all the profits from the work as compensation.