The no-fuss approach to wearing brights? Wear two at a time. Mix yellow with bright blue. Or cobalt with pink. It "grounds" the look and you can get away with two neon brights (which can look harsh by themselves) this way.
Below: Yellow bag with cobalt dress
Below is Looklet Model Jazz
Dress - Raasta
Belt - Marc O Polo
Handbag - Longchamp
Flats - H&M
Although I would've chosen much brighter selections, this is the best that I could put together. This is a more casual version of the rule. Bright orange and pink combined didn't clash being a combination of just the two of them. But having just neon orange or just neon pink alone could possibly become "eye sores" if worn wrong. Quite a tricky style, if you ask me. Again, with the balancing theory, two brights tone each other down. More than two brights at the same time need very careful analysis.