Many companies now market 'Vein Finder' products, but these products can cost over $5,000 (depending on quality and utility). That price tag is often outside the means of smaller clinics or facilities. This is a guide intended for hobbyists and DIY problem solvers -- not staff of a large hospital looking for high-end tech to aid in routine venipuncture.
This tool works by using near-infrared wavelength LEDs to illuminate the flesh at the site. The veins will appear as dark bands because they are more absorbent of this spectrum of light than the surrounding tissue. It is similar in principle to holding your hand over a flashlight (something we all did as kids).
Estimated Time to Complete: 3-6 hours (depending on your plastic cutting and soldering ability)
Estimated Cost: ~15-50$ depending on shipping/availability of free samples/if you need to buy solder, spare wiring, misc.
Below is a quick video of it working, moving it up and down my forearm. It's hard to document how clearly the veins appear because of my camera's minimum focal distance, but this ought to give you an idea (imagine no blur!):