Part of what make digital video a unique art form is that you have the ability to create an entirely new world for the audience. This is done through a variety of means, but what always ends up being drastically important is to effectively construct the scene you are shooting as a way of creating a believable area. Whether in the field or in the studio, knowing the elements of the set you are working with will help you focus on the correct parts or the action.
The floor can constitute a variety of materials depending on where you are shooting. If you are in the field this can be almost anything, from concrete to grass. In the studio it is traditionally linoleum, which can cut down on sound echoes and is still smooth enough for cameras to glide on. If you need to have the scene propped up even higher for filming you should use a riser, which is a fairly large and flat platform placed on the floor. You are not going to see the riser, so it is best to pick material that will reflect your function rather than aesthetic.
The background is going to be whatever is directly behind the main action. This could simply be the location you are recording at if you are in the field, or possibly a more illustrated backdrop if you are in the studio. Depending on the type of studio you are recording in you can use a variety of types of background dressings. A hanging background is exactly as it sounds, and is usually a hanging curtain that is either a solid color or graphical design to brighten up the backside of the subject. These kinds of background are usually used for news or interview filming that do not require a background that will help illustrate a story point.
If you are in a studio you are going to have several other types of set elements that you will be dealing with to construct exactly the type of scene you want. Columns and Pylons are often used to construct a set or to add energy to an otherwise boring set-up. Furniture and house dressings are the most common elements to add to a small set, especially one constructed by a home digital video producer. Since furniture has more character than generic set construction elements it is important to make sure that it is useful, appropriate, and will actually be interacted with in the scene.
The best thing to do once you have identified the elements you need to address is play around until you find what fits. Digital video filmmaking should be an experiment, so expect some trial and error.