In the image above I have INSERTED the PICTURE I am using in precisely that format...Insert and then Picture, browse for the file and choose it.
Once you have inserted your image you will Click on it to select it, which gives you an additional set of menu options. For PowerPoint, the options appear in the menu bar of the program for Publisher some of the options may also appear as a floating toolbar specifically for making changes and edits to the picture, depending on your settings.
In the image above, for Power Point, I will choose Format which appears after I select the image. Once I am in that menu bar item, I will select the option to Recolor, and then choose the little wand and corner bracket icon for Set Transparent Color and I will select that then click on the gray blue background of my image to remove the background color!
For Publisher it is a bit more direct in that once you select the image (by clicking on it) and once the Picture Edit Toolbar appears you simply click on the icon, then click on the background of your image. It won't very likely say the words Set Transparent Color as mine does for Power Point but the icon is the same. Below is an enlarged image of the icon, so you know what you are looking for.
So now that I have touch the background color with the wand, you can see below how fabulous the image looks!