Be sincere. You can fool some people but if you are smart you will not try it with an angry Scorpio. Apologize sincerely and without condition. Scorpio will spot a fake or insincere apology faster than an Aries will spot a diamond, so don't risk being hit with the infamous scorpion stinger by being insincere.
Ask Scorpio what he needs for you to do. While this is basic in most apologies, it's extremely important with Scorpio. This astrological sign holds grudges more than most but they are fair about it. As long as you have met the conditions of forgiveness, it's over. Until then you need to be on your guard for retaliation. Once he has declared the matter over and done with, you can relax.
Don't makes excuses. Even valid excuses and reasons for what you did will not be heard as anything other than a form on insincerity. You want to omit them until a later time when Scorpio mentions the event. When that happens, present your reasons and apologize again. It's over and done with but Scorpio is likely to get his stinger flexing when you mention your reasons. It's safer to offer a quick apology and remind him that you met his conditions and he said the matter was over.
Don't do it again. Whatever it is that you did, don't do it again unless you want to end the relationship permanently. Scorpio can be forgiving but only once for each offense. Scorpios rarely make themselves into doormats in a relationship. Trying for variations of a theme or splitting hairs is never a good idea with Scorpio.