Meconium is pretty tough stuff. It looks a lot like tar, and will be stuck to your baby's bottom as well as his diaper! If you are in hospital when your baby has his first bowel movement, a nurse may help you clean it up. If you are at home, or are doing it yourself despite being in hospital, you may be in for a little shock. After having cleaned two meconium diapers for my two babies I would advise you to clean most of the meconium off with wet wipes first. Open the diaper, but leave it underneath your baby, and wipe that little newborn bum clean as much as possible.
It is probably impossible to remove all that sticky goo with wet wipes, do you can then either give your baby a bath (no soap needed, just lukewarm water) or clean him with a (really quite) wet towel or cloth. The whole process may take quite a while longer than you expected! But don't worry not all of your baby's diapers will be like this! Once the meconium is out, changing diapers will seem like a dream. Infant poo is really no big deal, apart from that very first diaper. If your baby has not had any bowel movement at all the second day after birth, you should tell your pediatrician about that. Also check that your baby is peeing regularly.