Best way is memorize it. Colors are in order according to the colors of a rainbow except for Black, Brown and white, gold, silver. Get a visual image of the color spectrum in your mind then close your eyes and read off the colors.
Black, brown, red, orange, yellow, green, blue, violet, gray, white, gold, silver.
My college professor told us to remember it like this BBROYGBVGWGS but this never worked for me.
The best way to memorize this is write it on a note card and put it in your shirt pocket. Pull the card out about once and hour all day for a week and read the colors, by the end of the week you will have it memorized. About once a week for a couple of months pull the card out and read it. After that you won't need the card anymore.