The most chic way to pull off neon in the 2010s is to pair it with popular neutrals like taupe, gray or tan. A neutral color will temper the bright neon. Also, neutrals are classic, and neon is trendy, so it's fun to combine both styles. We even found a Neon and Neutral Pinterest board, if you'd like to take a peek at it for ideas.
The nice thing about pairing neutrals with neons is that the neutrals, at least, won't go out of style. (So they won't be a waste of money.) For the neon-and-neutral look, keep your accessories (shoes and bags) neutral and let just one neon piece stand on its own.