Veins can be slippery, roll-y little buggers. Go too slow with the needle and the target vein will literally roll to the side from light pressure, some kind of magical, evolutionarily-fit way to evade thorns, pricks, and accidental bleeding-out. Unfortunately, blood vessels have not yet evolved to tell the difference between life-saving IV antibiotics and malicious pricks.
Slapping the vein to make it pop really hurts (especially if the instructor does it), more so than the needle poking around later, or the bruise that will soon form.
A "blown vein" is one that has been ruptured and is now bleeding beneath the skin. This often forms a hematoma, a green, blue, or darkened, painful area. For photographic documentation, see classmates' social media pages/stories.
Venous blood is very dark, deeper than Merlot, looks like poison.
"We have a bleeder!"
This is probably the only time seeing blood will make a student nurse happy--a smooth IV insertion, the "flashback" of red in the plastic chamber. However, it's not a successful insertion until blood actually returns to the syringe, the saline pushes in, everything is properly connected, sterile, and taped correctly, with minimal scrambling, patient complaints, or instructor eye-rolling.
If all else fails, hospitals have vein finders, which are super awesome and make tattoos and non-venous-bits fluorescent, which might entertain the patient briefly while a third nurse takes a stab at one of his last possible arm veins before a doctor's order needs to be obtained to move on to lower extremities.