The free downloads for each blue smiley you always find below the description of the big smiley picture. Not for all the smileys all formats are available.
A quick overview of all available smiley formats you can find in the List of smileys.
The downloaded images in PNG format you can use for your website, text documents, etc.. Most modern programs can represent these graphics.
After downloading the wallpaper it is in the folder you specify. On Windows, you can open the folder in Explorer where you saved your smiley. Then you click on the smiley file with the right mouse button and choose Set as Desktop Background. Depending on your Windows version, the name of the menu item to select the smiley as wallpaper may vary.
In the settings menu of your Android smartphone select your smileybackground: