Services such as Photopin allow you to search for photos that can be used freely, but even then, in most cases you are required to attribute the image to the author in your blog post where you use it. Once you find the image that you like on Photopin, when you go to download it, the code for attribution appears.
Copy this and paste it with the image. If you click through to the image source, and it takes you to the page for the photo on, say, flickr, you can see the license the author published it under
with an explanation of what each license requires you to do.
You should always credit the source of your image regardless of the requirement.
Another useful service is The Noun Project.
You have to sign up for a free playground account and can then download and use icons in your blog which are in the public domain or attribute ones that require it.
A nice example of how these can be used effectively can be found on the Hack Education blog. While you’re there, check out how the author adds a license to her posts as well, this might be something to look into at a later date.