You will need:
- Xbox 360
- Image to use as your background
- USB thumb drive or CD. I recommend a thumb drive, they're easier to use and using a write-once CD just for a background is dumb.
Step 1: Get an Image
You change the format by using an image converter, or by opening it up in an image editing program and saving it as a different format. Don't use Paint if you don't have to, it applies some nasty compression to images, which makes them look like s***.
As for resolution, if the Xbox and your TV display it right, you should only need an image with a resolution of 640 by 480 pixels if you're not using a HD display. If you're using a full resolution HDTV (the biggest NTSC standard), you should need an image with a resolution of 1920 by 1280. If your image isn't the same resolution as the TV, don't worry. Your Xbox will scale the image to fit your TV. But an image that's the right size will look much better. Don't be a dumbass and use a tiny 100x100 image.
Step 2: Set the Image As Your Xbox 360 Wallpaper.
Here is the image I am using on my PC and Xbox at the time of writing this, and here is the post with details, by me.