Put neon to work. Wear your neon with your most conservative office attire -- a suit, a button down, a sheath dress.
Make it retro. If you don't want to look 80s retro, try to look 50s or 60s retro. Which leads me to my next point...
Be a lady. Ruffles, lace, peplums and other romantic details provide contrast to the harsh nature of neon. One of my favorite ways to wear the trend is a neon cami under a black lace tank.
Avoid the hyper-casual. If you want to avoid looking like a teenager, don't wear your trendy neon with the same casual clothes a teenager would wear -- sneakers, torn jeans, graphic tees.