Have a lot of talent and sing well. Sure, this will impress any judge, but it's a must when it comes to impressing Simon. He is well-known as the harshest judge and if you don't sing well, you can forget receiving a positive comment from him.
Make sure your performance matches the song and the song fits you. Simon will always point out when things don't seem to fit right and make comments like, "That went together like chocolate ice cream and onions." If you sing a song that is good for your voice and you look the part as well, Simon will compliment you.
Be real and original. There is nothing Simon hates worse than a performance that he will equate to karaoke or a cabaret. He will also point out if he felt you were just copying the original song and he'll likely tell you the original is better. But if you do your best to be original in your performance and stand apart from previous performances of the song, he'll notice this and appreciate it.
Show him that you listen to his criticism and make improvements each week. Simon will always have negative things to say, but you can take his comments as a learning experience and use them to improve. If he gives you advice, show him with your performance the next week that you took his advice and used it to make yourself a better singer.