The following is my tip for hitting a vein. As soon as the needle pierces the skin, pull back on the plunger very slightly, which should create very small vacuum air bubbles in the syringe. Then, continue to insert the rest of the needle extremely slow. That slight negative pressure in the syringe will cause the syringe to fill up with a plume of dark blood when you've hit the vein. Once you see the blood pouring into the syringe, STOP ANY MOVEMENT. Wait for the blood to stop pouring in and slowly push on the syringe while keeping everything else still; by now, you already know what a miss feels like, so watch for it. This is an easier way to find a vein because you have less of a risk of piercing through the other side of a vein, and also, you won't be disappointed with the lack of blood in the syringe when you think the needle's in.
Also, many first time users have a problem of inserting the needle too shallow. Especially when you raise your veins, it looks like your vein is right under the skin and you can hit it without a problem. They're actually a little deeper than they look, so make sure you have the proper angle.