How can you make those red veins on your eye ball go away?

Bloodshot eyes. Get more sleep don't smoke especially pot use visine temporarily or you'll get rebound hyperemia ie will look worse when you stop use artificial tears use sunglasses use iopidine (used for models in photoshoots, needs a rx, is a glaucoma drug) get lasek if you overwear contacts if horrible these can be surgically cauterized but sometimes they return.
Not too easily. Veins are there to nourish the structures of the eye but at times they can become prominent if there is dryness allergy etc. Otc moisture drops used regularly can help cut down the redness. If there is very prominent redness an ophthalmologist should be seen.