Although the shoulder press can be performed on a machine, with a barbell or with a dumbbell, the last option is probably the best.
As with most dumbbell exercises, you need to start out with light weights until you are capable of getting the technique right.
Clasp a weight in either hand. Stand comfortably, about shoulder width apart at the feet. Raise the dumbbells to shoulder height.
Make sure you are steady and balanced through the core.
Now, push the dumbbells towards the roof and slightly forward. At the peak, the dumbbells should touch directly above your head.
Lower to shoulder height, and repeat.
You can also perform this exercise when seated at an incline bench. Some people find this gives greater support.
Remember that you can easily damage your shoulders if you do this exercise incorrectly. Try to stick within a safe range of movement.
Aim for three sets of eight, varying the weight based on your strength.