I need to replace three sections of vinyl sideing that was damaged when my gas grill caught fire. Would I start at the top piece or bottom piece?

In siding section of HD or Lowe's purchase a siding tool. The siding tool is just a thin strip of metal about 1" wide with a little hook on one end and curved so that you can grip it. Use this tool by sliding it up under the bottom edge of the first undamaged piece siding above the damaged siding. Do this close to the end of the piece of siding. After hooking the bottom edge of the siding pull down and out to separate the siding. Remove and replace the damaged siding. When replacing the top piece of siding use the dame nail holes in the sheathing. That way you will be certain that you it at the correct height. Get it to high and the piece above that you did not remove will not be held in place. Get it to low and you won't be able to snap the piece into place. Reconnect the piece above that you did not remove by striking the bottom edge with the palm of your hand.

How far up is the burned area? You can just replace them by using a zip tool to release the siding. The only problem is that you it can sometimes be difficult to nail the last piece and then snap the top piece over it if the installer didn't leave enough "drop". You would use the same zip tool to reinstall. The best way is to take it down from the top and then nail up like a new install.

Don't nail the siding tight! It has to be able to move in the slots.