It sounds like you have spider mites. Take a piece of white paper and put it under the leaves where you see the spider webs and shake the plant. The mites are usually on the underside of the leaves. If you have red or black things hit the paper then you can see them and they will leave a residue when you crush them with your finger. Also, the leaves are browning from the bottom of the plant up indicate spider mites.
Getting rid of them is the hard part. The best product is Avid which has a systemic action but is VERY expensive to purchase. Next find a product that says will kill spider mites, and maybe some others can make recommendations to you. Whatever you use you need to use it three times about three days apart so you kill them in all stages of development. You must spray on the under sides of the leaves. Then spray for them weekly as a preventive measure.
If not killed they will kill every plant they get on in your garden.
Take a look at the DS of Georgia newsletter for June 2007, Page 4, and July 2006, page 2 for a discussion of spider mites and other bugs.

Here is a link that might be useful: Dahlia Society of Georgia