Step 2: Measure the window and cut the mattress
Take the cover off your mattress to expose the foam core. IKEA Sultan mattresses have a grid scored into the top half of the foam. This turns out be a fantastic guide for the first cut. There are a number of implements you can use to cut (an electric carving knife, a saw, etc.) but I went with my trusty sharp kitchen shears. You'll notice it came out pretty ragged--look for something better to cut with if you're a perfectionist/pressed for time.
Save the top piece! You can use it to make cushions later.