Microsoft Windows
First of all: You can use an 1024×768 resolution wallpaper on an 800×600 display, and vice versa, however using an 800×600 wallpaper on a 1024×768 display will become blurry.
Putting a wallpaper on your pc background: Right-click on the wallpaper once you’ve opened it from the wallpapers page, then save it on your hard drive. Now click on the start menu (bottom left of the screen) and go into the ‘Control Panel’. Double click on ‘Display’ and click the tab at the top which says ‘Desktop’. Now click ‘Browse’ and locate the wallpaper you’d like. Then select whether you’d like it Tiled, Centre or Stretched. If using an 800×600 screen I recommend using stretched, however when using an 800×600 resolution wallpaper on a 1024×768 screen I suggest using the centre option as it will prevent the image from blurring. Now just click ‘Apply’ and then ‘OK’ and you now have a new wallpaper!
Mac OS X
Chose the wallpaper in the wished size (widescreen looks better for widescreen, the normal wallpapers would be cut, but can used, too) in your browser, click save as… and save it somewhere on your harddrive. Rightclick (or ctrl + click) onto the desktop and chose the changing background option, here search in the folders for your wished wallpaper, click onto it, and chose the best looking option from the dropdown. If you have a widescreen desktop and a widescreen wallpaper and a huge resolution, desktop filling would look best, for a small 800×600 wallpaper maybe the centered look with a similar background color would look better. Just try it out!