It is pretty easy to detect the state of door/window embedded switches with an arduino. Wiring (or wireless communication) between the switches and the arduino would be the hardest part. The rest is clearly possible, but needs to be fleshed out before anything can be designed.
It is probably possible to send SMS messages via some internet service, such as Skype. For that, either a wifi or ethernet shield might be appropriate. I suggest a wired connection unless you must use wifi. Alternatively, a gprs shield could connect directly to the a cellular network to send SMS messages. As another alternative, you might post messages to Twitter or similar.
You'll also have to figure out what messages you want to send where under what circumstances, and how you would update these rules once programmed. Will you need to receive messages, or take any local action besides passive monitoring?
To address these kinds of questions, you might imagine that you are about to purchase an off-the-shelf product that will do what you want. Write a user's manual for that imaginary product. I offer that as the first of your step-by-step instructions.