Open the diaper, use the inside front flap of the diaper to wipe off any poop, fold it over and rest DD's still-dirty butt on top of it, use wipes to clean her off, place the dirty wipes onto the dirty diaper as I go (I fold them over so DD isn't sitting right on top of the wiped-off poop), then I bundle it all up and throw it out once she's all clean. Then I grab a clean diaper - I either leave her clean butt right on the changing pad, or I'll hold her ankles up the whole time. I usually also get one more clean wipe to make sure she's all clean before putting on the new diaper.
When DD was brand new and kept peeing or pooping during changes, we started keeping burp rags or folded receiving blankets on the changing pad. That way if she dirtied it, we could just throw the dirty rag/blanket in the hamper rather than having to swap out the entire changing pad cover.