Dealing with damage done to a skylight can be tricky. The main reasons for this are that rain, and anything else landing on the roof of your house can fall through your skylight, and reaching the damage in the first place is a difficult task. If you can see that there is simply a hole in the glass, you are relatively in luck. Replacing only the glass won't cost more than a couple of hundred dollars, and a specialist company can do it in less than a couple of hours. It is naturally an inconvenience, but not as much as it would be if the frame was damaged. If this was the case, the frame, also, would have to be replaced, costing somewhere around $1000. This is a much greater hassle, and whilst a specialist company shouldn't take too long with it, the cost is the biggest problem.
While you will now have a good idea of how much a repair will cost, and how long it will take, there are some measures you should take to prevent water getting into your house. Most people will simply place a bowl below the
damaged skylight, and think that is all that needs to be done. Not so. If the rain coming through the skylight is moving to to the side, not simply falling straight, it may completely miss the bowl. Luckily, there is a simple way to stop this. Just place a towel over the hole in the skylight. The water will drip or flow from the bottom of the towel, directly into the bowl.
I hope this helps you to understand how you can prevent water from getting into your house if your skylight happens to be damaged.