The first thing you need to do is to set a goal for yourself. In order to do that, determine the time it takes for you to ski from the top of the slope to the bottom. Either measure the time yourself using a stopwatch, or get someone to measure your speed for you. Your current time will help you set up a new goal. Make sure that you set up a realistic goal instead of aiming for a time that a recent Olympic gold medallist may have set.
Once you have determined the time it takes for you to reach the bottom of the speed and set up a new target, you need to start working on your physical strength and stamina. You can increase both your physical strength and stamina by including cardiovascular exercises in your daily routine. Try to jog for at least 30 minutes, ride a bike, swim or walk every morning. Also try internal training to boost both your strength as well as speed. Working on your physical strength and stamina will help you in increasing your speed on the slopes.
Training yourself off the slope will undoubtedly contribute to your performance on the slope, but what you actually do on the slope is what would eventually play a primary role in helping you ski faster. For this, you need to work on your stance, giving a greater role to your ankles while skiing. To do that, push your shins right against your boots, while extending your arms out in front and keeping the parallel to your chest. This will help you to maintain balance.
Adjust your stance even further by pointing your chest forward and positioning your upper body in a way that it faces downhill.
Do not forget to take a break from training to give your body some time to rest and regain strength. Your body will start becoming weak and show signs of weariness if you exert yourself too much. However, try not to take a break from cardiovascular exercises.