Above is a screenshot of the custom twitter background I created a few days ago for my twitter profile page. Custom backgrounds are awesome because they make your page stand out from the crowd and allow you to convey more information than you'd be able to without one. When I was trying to create my background, the guides I found online were outdated. These instructions are up to date with the December 2012 version of twitter.
1. Open your favorite image editing program (I used gimp 2) and create an image that is 1920 x 1080 with 72 DPI.
2. Create the image that you want to be your background. Any information that you want to display should be placed on the left, top side no more than 225 pixels away from the edge.
3. Save this image as a .jpg.
4. Go to twitter and click on the gear in the top right corner. Then click on "Design." (see pictures below)
5. Click on "Change background" and upload your photo.
6. Click save changes and you're done!