There are many ways to find photos online which you can use legally on your blog. I have listed sites which host free images. The most common licensing used for free photos are Creative Commons licenses. If the photo is licensed under CC0 aka public domain, they can be used without crediting the source. The public domain images are the most flexible, of course and you can find them from multiple legal and high quality sources. But using other CC licenses will widen your options. There are several different licenses and it may be a bit confusing to figure out how to use these photos.
When you are about to use a Creative Commons photo it's a good idea to read through the license. Usually CC licensed content features a link to the license thus you can check the details on it. For instance on Flickr there are lots of CC licensed images. On the image page you can find the license from the top part of the details listed under the photo (on the mobile app they are located in a different place than on the web version). When you click the "Some rights reserved" text you will be directed to the licenses human readable summary. It will give you an idea of how the license works and which rights you have.
Other license than CC0 always require attribution. This means you must tell whose photo it is and provide a link to the license. Often it's appropriate to provide a link to the original content. It's a good idea to check if there are any guidelines by the creator of the photo about how they want to be credited. You also must tell about any changes you may have done to the photo. Note that you may not make changes to all the CC licensed photos, this depends on the license. But which ever license you are using you must always credit the creator. For instance if you used a CC photo from Flickr, the creator is not Flickr but the person whose photo you are using.
At this point I must note that some idiots are licensing their photos under CC licenses and then telling you to ask if you want to use them. I most often don't use those photos, because they obviously don't understand how the CC licensing works and it would be more trouble to me try and teach them in case they would come after me for using their photos. Basically when the photo is CC license you don't have to ask for a separate permission to use it as long as you use it the way the license dictates.
As I mentioned before there are several different licenses. All require the attribution (except CC0) but there are other variations. The simplest licensing only requires attribution and it's called either (Creative Commons) Attribution or in a short way CC BY. Attribution-ShareAlike (CC BY-SA) requires attribution and you must also share the modified photo under the same license. Attribution-NoDerivs (CC BY-ND) means you cannot make changes to the photo but you must share it as is. Attribution-NonCommercial (CC BY-NC) makes things for a blogger a bit more complicated. There appears to be a bit of debate on which kind of use is commercial. In case you want to stay on the safe side you can think that trying to have or are having financial gain from your blog (selling ad space, using AdSense, selling your products or services) makes your blog commercial. Attribution-NonCommercial-ShareAlike (CC BY-NC-SA) is the other one of the more complexed licenses. Again I recommend steering away from photos licensed under it in case there's any chance someone might see your blog as commercial. The photos licensed by this require attribution, cannot be used commercially and derivate works must be shared under the same license. Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) also requires attribution, cannot be used commercially and you cannot create derivate works with it. My personal take on this is to try and make sure the photos are licensed under CC BY or CC BY-SA in case I want to use them. Take a closer look at the licenses on the Creative Commons site.
Things get a bit complicated when people change their licenses afterwards. However the licenses are actually irrevocable (cannot be changed) thus if the license was changed afterwards you will still have the rights that were applied when you first used that photo. So if you found a photo licensed under BY-SA and inserted it in your blog post and a month later you found out the photo creator had relicensed it under BY-NC-SA, the first licensing should apply on your blog post. Of course if thing get really hairy it's best to just give in and remove the photo from your blog post. Unless you've got a really good lawyer.
The credit must be given somewhere close to the photo and must be easily found and seen. However when you insert the photo on your blog post by using WordPress' Featured Image or other similar way it might be easiest and the least confusing for you to add the credit in the end of the post rather than right below the photo itself. The ideal attribution, according to CC Wiki is "Photo name linked to the original photo" by Creators Name (or nickname) linked to their photo stream or website is licensed under Creative Commons license name linked to the human readable license deed. In case you modified the photo in any way, mention this too. If we follow the best practices and do the attribution in English that would go something like this:
There are other ways to make the attribution, the above example is the ideal format. Creative Commons licenses come with a clause which points out you must make the attribution reasonable, thus you may not have to follow the ideal format in case it's not reasonable. Different languages make that a bit more complicated. Trying to translate the ideal attribution straightforward to Finnish is close to impossible. At least make sure you link to the source (which should be the original photo basically), mention the creator and link to the license.
I'm not a legal advisor nor have professional degree in law. Please see Creative Commons for more information.