Flash unit on my Nikon

Any one have any ideas on the best way to eliminate the shadows using the hot shoe flash unit (or the onboard) flash on my SLR digital camera (Nikon D80)? I have watched the better bounce card video and wasn’t too clear on what he was getting at. It is a very tedious video clip and difficult to sit through! This was an issue when I took some posed wedding pictures recently. The couple said the shadows were OK with them but bothered me a lot. I have been taking pictures at small weddings of friends in my church for a long time (for free) so I don’t expect them to complaign too much.