Webcams can sometimes be more susceptible to glare from lighting...
Otherwise, any of the lighting suggestions I've made elsewhere on this forum apply.
At most grocery stores, you can pick up a large sheet of colored poster paper for about 1 dollar. A sheet of green or light blue works well as not only a backdrop, but a surface for setting up. At some places (walmart I think), they even carry 2 sided Red/Yellow paper. Paper is vulnerable to folds and oil, so avoid that or you'll have noticeably tarnished paper in photos.
If you are somewhat artistic, you can paint a texture onto the paper with acrylics and then seal it with some type of acrylic varnish. Currently, I've been trying without luck to buy used vinyl marble textured flooring remnants on craigslist from people to use as backdrops.
Most people simply drape the paper, taping it to a wall and setting figures and scenes on the part that rests on the table. This works very well for small scenes.