Mark Check two posts down on shooting on the cheap. Simply put you just shade the background or put it far enough away that the light falls off or both. In this case I did both. It's very easy when you use direct light. You just don't light the background.
When you use a photo booth or a panel it gets more difficult because the panels spread the light. In the photo of my set up you see I have 2 panels. The second panel also wants to bounce light into the background. You have to control this light.
The first thing I do is block the main light from hitting more of the panel than I want or from hitting the back ground. I do this quite often by simply putting piece of cardboard (we have lots of foam core so I use that) between the light and the background. On my pro lights I have what we call Barn Doors. They fit on the lights and close just like swing doors. What I did for this shot was make a home made grid out of cardboard tubes. That narrows the beam of light so I can control it.
After griding the light I still had a background that wasn't very dark so I move the background back. I know that's not an option for most people but putting the background on moveable stands was one of the best things I did to speed up getting a dark background.
To put it simply light falls off as it gets further away. Do you remember your f stops, 2.8, 4, 5.6,8, 16,22,etc. Well if the background is 2.8 feet away and I move it back to 4 feet away I just lowered the light that hits it by one full f stop. It's that simple. Now add in a little shadowing and you can easily lower the light on the background by 2 or more f stops.
Of course you could just buy a graduated background but they are expensive and scratch fairly easily. Shooting from a low position helps. When you shoot from a higher position you naturally don't see the background very far back and it's much harder to get a fade background. Bowls with lots of figure inside are difficult because of this. I shoot them from a higher position so you can see the inside. to get these to fade I have to use a direct light with grid so it forms a circle around the piece. Small grided lights create hard shadows that make filling in the shadows more difficult.
I'll use that concept of the f stop numbers when describing problems with fill lights and backgrounds so keep those numbers in your head. They are handy