I have just purchased a home in Norfolk VA that has asbestos siding. I would like to find out if I can remove it, and replace with Certianteed siding panels, or can I place the panels directly on top of the original asbestos.

The removal and disposal of asbesos will be very very costly. It has to have certified disposal people and there are very strict laws. As long as the fibers do not get airborne ( liablity to workers if it does) you can put other siding over it ( but watch as it often cracks into pieces easy (if it is the type I am thinking of)

It would be best to get some prices from licenced contractors who are insuranced as to the cost of doing it both ways.

It far better to wrap up the house and place siding OVER asbestos than it is to do a teardown of asbestos... the hazards involved and the costs involved do not justify the removal(ie.. licensed asbestos contractors.. permits.. etc... )

I would recommend wraping and siding over it..

Here is a link to read more about this
Asbestos Roofing And Siding On Homes: Environmental Health in Minnesota

Check w/ your local township about any restriction in you personally removing it. Some areas have no restrictions on the homeowner removing it themselves. When you get a dumpster ask the waste company if they have any policies on asbestos.
IF any restriction you may have to do what Fr. Chuck said.

I just recently did some demolition work and rented a dumpster where it clearly stated NO HAZARDOUS MATERIALS... and asbestos was 1st on that list.. so I'm not sure you're going to find a dumpster rental company willing to deal with asbestos... to many problems with hauling and covering without letting it escape from hauler... a licensed asbestos contractor is your best bet if you have mad amounts of $$$$$

Because asbestos in certain forms has been determined to cause serious health problems, the DEP regulates the removal, collection, transportation, and disposal of Asbestos-Containing Materials (ACM). DEP does not regulate the removal of ACM from private residences unless the residence is an apartment with five or more units. Contact your township or borough to find out if there are any local regulations.

This is from the Dept of Environmental Protection asbestos page. Used as an example. Like I said before contact your township and waste company before you shell out the money.