either in the soil or in the water. usually the water is dyed and it is then taken up via the roots. [certainly for cut flowers its in the water. my girls have done it before with white spray carnations and food dye. cut the ends of the stems and then they take it up with the water]

You can also get floral spray paint online. Requires practice to get the desired effect.

https://www.wholesalefloral.com/Floral_Spray_Paint_and_Dyes_s/44.htm

The stems are injected with dye and the hole plugged with wax. I detest man made coloured plants, especially orchids. I was given a blue one to rescue and it hasn't stopped blooming for the past two years with the most beautiful large white flowers.

There are naturally periwinkle blue Phalaenopsis orchid species and hybrids (P. bellina var. coerulea) but they haven't hit the mass market yet, probably due to small flower size.

Thanks to all of you who answered. I too Cammomile am not keen on the artificially dyed ones and much prefer my plants in the garden than indoors, but it was a gift!
It has the loveliest white flowers, so why dye it?

Thanks Tug, I looked at your suggestions and got lost in the beauty of them all - now if I had an Orchid house!!!!

I knew they dyed flowers Seaburn by putting dye in the water, but wasn't sure how it was done with plants.

That's amazing Bathgate, the things that you can buy to alter Nature - live and learn.