Everyone gets dizzy to some degree when they get up suddenly from a supine position (laying down) or even sitting. When significant, this is called orthostatic hypotension. The most common cause in a 'normal' person is because the veins in your legs hold more blood proportionally lying down than when standing and walking. When you suddenly stand, the blood returning to your heart in insufficient to supply your brain momentarily (i.e. your cardiac output decreases.) The answer is, indeed, getting up slowly.
In addition, keeping well hydrated may help; Since in a supine position the venous capacitance is high, move the muscles in your legs - all of them from your toes up - to increase blood return to the heart. Start by pointing toes (entire foot) down then up a few times, rotate your ankles, stretch your legs, bend your knees, squeeze your knees together, push them apart against resistance, etc. If you're on your back, roll over once or twice and back again. Then see if all that helped.
If this only happens in the morning, keep water by your bed and drink a couple of glasses of water (about 16 oz) before getting up (ideally up to 30 minutes before), and elevate the head of your bed.
Get enough exercise.
There are a lot of medical causes of dizziness on standing as well. Because of your age and how long this has been going on, one would need to do a few tests to see if your nervous system is slow to respond to sudden changes in cardiac output (this is called autonomic dysfunction).
If this is bothersome enough, a more in-depth evaluation should be done. Only a good exam by a doctor can tell if it is significant enough to warrant further investigation. If you're unhappy with your doctor's approach, get a second opinion.
Above all, take @DoctorWhom's advice in her comment.
the paper below discusses some scary things. Please keep in mind that due to your age, you're unlikely to have many of these conditions.
Preventing and treating orthostatic hypotension: As easy as A, B, C
