Gemenigirl1963 has provided you with on-the-money advice about keeping hydrated before the IV.
Wash your arm.
Drink at least a liter of fluid, preferably with an electrolyte.
Also drink a cup of two of coffee to raise your blood pressure, or have a coke.
Swing your arm in a circle several times BEFORE the torniquit is on.
Pay attention to who gives the IV. Sadly, there are many physicians and nurses who seem incapable of performing this simple task. Don't hesitate to ask for another technician.
Thirty years ago I used thermal night vision devices to ALWAYS find a vein. The differential in temperature shows the vein pattern. Someone patented this two years ago (it's an invalid patent it's public domain) and it's now the flavor of the month in many hospitals.
by the way - I noticed your name - I have a good friend whose last name is Banerjee!
As the nurse or tech to use one of those little warming pads they use for pediatric patients before they attempt the stick. This may be enough warming for your veins to pop up since you say they do it on their own when you're out in the sun.
It might also help to make sure you're well hydrated before you have to go for bloodwork or have an IV inserted. If you're dehydrated, your veins will not be as visible/easy to access.
I can empathisize with you - my veins are HORRIBLE and simple blood tests usually end up resulting in numerous needle sticks before they get it. Whenever I have to go into the hospital, I normally end up having to get a PICC line because my veins are so bad and they have such trouble getting IVs started.