Bobbi gave very good advice. Another tip is to let gravity work for you-allow the arm to hang dependent for a minute or two, over the edge of the bed. Then, put your tourniquet on before lifting the arm to search for veins.
The most difficult folks, by far, are the grossly obese. You can't see a vein, and you can't palpate one. My experience is to try to smooth the adipose tissue horizontally across the ac, looking and feeling for a vein. For some reason, that worked well for me.
Another one is to remove a person's watch. Usually there is a medial radial vein that the watch band covers and protects from tanning, etc.
In elders, don't be misled by their large, prominent veins. They ysually are plaqued and sclerotic. Try a 20 or 22 in the hands, wrists, and forearms.
In babies, look at the dorsum of their little hands. Again, you may have to run a thumb horizontally across their pudgy little hands to push the adipose tissue aside. Another way is to put the medial aspect of their ankle against the palm of your hand. Then, with the other hand, flex the outer aspect of the foot and ankle downward, and the veins on the dorsal aspect of the foot become evident. Depepnding upon the age of the child, do not use too big an angiocath. Start with a 22 or 24. For neonates, a 26 may be necessary. We used to keep those on the Pedi Crash Cart.
I was never a fan of IV teams-always had to wait on them. Working in ER, it is much easier to just get your vein, draw labs, plug in your solution, get your EKG, and etc.
In the last hospital I worked in, the ER nurses were called to start difficult IV's on the floor.