Some medical personnel are better than others in succeeding when a patient has small veins. For starters they should use a tiny needle, like they use on babies. Many times when one medical person cannot succeed another one will have no problem. Feel free to ask for someone else to do the draw.
I don't think that you can really increase the size of your veins. It is easier to get a stick, though, if you are well-hydrated. So if you can plan ahead, make sure to drink lots of water so you aren't dehydrated at all. I'm usually an easy stick, and I recently went in for dehydration after a stomach illness... The nurse only stuck me twice for each of the two needles, but she really spent a lot of time rummaging around in there trying to get into the vein. Dehydration is definitely not good for getting needles into veins!
I agree the dehydration makes it much more difficult make sure you drink plenty of fluids before. My 2 yr old daughter had to have blood drawn when she was very sick but she was dehydrated and they had to start an IV on her it took them 12 tries. It was awful then she pulled it out. But A pedi nurse got it back in one th 1st. I was so glad.
Hydration sounds like a good idea. However, I think it is just incompetence on the part of a lot of the phlebotomists that they can't find a vein and they cover that by blaming it on the patient, who usually doesn't know any better. If they are fooling around and blaming your veins, stop the process and ask to have the most experienced person in the dept. work on you. Also, many hospitals have an "IV Team", usually composed of experienced highly skilled nurses - you could also ask if they have one, and if so, for them to insert the needle. Patients and parents, if it is a child, really have to speak up for themselves and show that they will not put up with less than excellent care!
I have the same problem when I have to get blood drawn, Ive noticed for me the best vein is in my hand/wrist area. You could try asking the nurse if she could use veins anywhere else besides your forearm and maybe have better luck.