A lot of good advice above.
To risk stating the blatantly obvious, your choices come down to not letting your lights directly or indirectly fall upon the backdrop or, if they do, having what light falls on the backdrop be overpowered by other lights or be so little it isn't relevant to the exposure.
Looked at in this way, you can see how all the advice above makes sense. If you use a grid on your source, it limits the light coming out of the modifier, making the light coming out less wide (kind of like narrowing a flashlight beam). This makes it easier not to hit the background with the beam. If you put in flags, you are basically blocking light which would hit the background. If you are feathering the light, you are aiming the light so it doesn't fall on the background. If you are using a darker background (black velvet is about as dark as it gets), you are reducing the amount of light the background can reflect (with any luck to the point where the exposure doesn't pick it up). Moving the subject further from the background either changes the relationship to the lights so the light (and hence the shadow) falls before the background or the light has faded enough before it hits the background. If you aim lights at the background behind the subject, you are overpowering the light which is casting a shadow.
I bring all these obvious things up because it is much easier, at least for me, to only need to consider a basic idea rather than run through a list of things which might work
. It also helps me see how I can change the relationships between light, subject and background.
Another cool trick is that moving the light source closer to the subject reduces how much hits the background, relatively speaking. We often think the further back we pull the light, the less gets on the background. But it's all about how close it is to the subject and how many times that distance it is to the background. It's the relationship between the two distances which counts.
The reason is that there is a larger percentage hitting the subject, who is closer, which is what you expose for. Light falls off more quickly than the distance.
If you can get the light one foot from the subject and they are seven feet in front of the background, there will be six stops of difference (plenty for it not to matter if you are exposing for the light which is one foot away). Even if you only have 4.6 feet, it is five stops. If you have three feet to the background from your subject and the light is one foot away, you still have four stops of light difference (which is 1/16th the light)--quite a difference.
The technical name for this, if you want to look it up or do calculations, is "the inverse square law."