http://www.recover-raid.com/failed-RAID-help.html

Does it matter which order I plug the drives back into the RAID? If so, is there any way I can tell which order the drives were originally in?
YES. Do NOT change positions of the drives and do not move them to different ports. I'm guessing all drives are the same make/model. If you didn't document their original positions, then I'm not sure how you would determine their order.

And finally.... do I have to issue some kind of special command or something to my RAID card to rebuild the RAID, or is it an automatic process?
It probably wouldn't be automatic, since you are replacing a drive. You would need to add/activate the new drive to the array. You didn't say what RAID controller you are using. You'd need to look up the manufacturer's documentation.