When changing diapers, put a fresh one underneath first
Here's how Liz simplified diaper changing way back when:
When my daughter was a little baby, we always pulled her outfit up and away from her bottom during diaper changes and then laid out a clean diaper under the dirty one before beginning. This little trick saved us from constantly messing up the outfit or the changing pad. Though you sometimes end up with a "wasted" diaper, as first-time parents, we preferred that over going through the stress of changing baby's clothes.
Warning! Graphic diaper description ahead!
I'm still in diaperland, so here's what I do: When there's poop, I open the diaper, then wipe the butt in question from front to back with the inside of the diaper, then fold it over and tuck it under said butt so only the clean outer portion of the diaper is touching the baby (and the changing pad is still protected). You'll be relieved to know there are no Flickr photos associated with my little howto.