I only have a backgorund on one of my tanks, and it is one that I got from someone else. From what it looks like to me, the person used tape to get it on, and did a fine job of getting it on without air pockets, too.
most of my tanks have the background taped onto the exterior
on one tank I have used silicon and attahed it to the inside.
I have found this to be far better in reguards to lighting up the
background, but the draw back is I had to wait for 72hrs before
filling the tank with water.
Mine is on the outside as well, I tried the tape but it just looked really dark. I then covered mine with Vaseline(petroleum jelly) and stuck it to the back then used a credit card/scraper to remove the air bubbles. It stands out much better, if I did it again I would try and heat the vaseline first to thin it out so it spreads better.