The only difference is the starting and ending position. Start by holding both dumbbells side by side near the top of your chest with your palms facing your body. Now, rotate your palms outward as you begin to lift the dumbbells. The rest of the movement is like a traditional shoulder press. Simply continue to raise the dumbbells up until you make them meet overhead.
Arnold presses are a great variation of the shoulder press and work the entire delt quite well.
Until you get the hang of these use a lighter weight than usual. Soon, you will be able to use as much as you do for a traditional shoulder press. Slowly raise your arms to the side until they are at an even level with your shoulders. At this point your palms should be facing the ground. Slowly lower your arms back to the starting position.