If it's original, it will contain asbestos. Asbestos can cause damage to your lungs if you breath in its dust. Other than that, it's not particularly dangerous. It's less dangerous than a lot of stuff you probably have around your house. The key is to not generate and breath dust.
The heatshield comes off by removing the screws and fender washers that hold it to the firewall. Get it wet first so you minimize dust, and take the screws out. Have a plastic bag ready to put the heatshield in. If you get any pieces on the floor, wet the area and sweep them up. When you have all the pieces off and in bags, put them in a second bag. Then you can throw them away.
Asbestos is a naturally-occuring mineral. It makes up serpentine, the California State Rock (which also contains mercury).