The most typical mistake is, that the template is not Minima, all my backgrounds are designed to work with Minima template. To change the template, go to customize (right upper corner).
Pick the Minima template, it's the first one. With Minima the whole background looks like it should look.
One other quite common mistake with the headers or the buttons is, that there is not transparent background.
The images with transparent background are in .png format, you must remember when you save them to your computer, that you save them in .png format, if you save them as .jpg, the background will be white.
An other thing you must remember with transparent background images, that you don't let Blogger shrink them, make sure you don't have check on "Shrink to fit". I make my headers and buttons right size to fit your blog without shrinking.
I'm not sure if I remembered everything, feel free to ask more, if these instructions don't help.
This has nothing to do with posting the images. You can post also images in .png format to your blog posts, and then you can choose there any size you like, the background will remain transparent. The right size is only important with the header image and the images you add to your sidebar with image gadget.