Cut the bottom of the rose stems into however many colours you will be using. For example, if you have three colours, cut the stem into thirds.
Place each cut stem into a different colour. Once all flowers have been placed into the food colouring, secure the roses into a bouquet with ribbon or string so they don't fall over.
Leave the flowers in the food colouring for around 24 hours. This is subjective to your personal likes, so there is no real set time-frame. When flowers look good to you take them out. Keep in mind, the stems have been damaged and flowers will likely begin to wilt within 48 hours.
Once you're happy with the colours, take the roses out of the food colouring. Have a vase with fresh water ready ready on hand. Taking each rose individually, cut the stem diagonally above where the stem has been sliced. You a sharp knife or blade to achieve a clean cut. Do not use a serrated knife, you want a nice clean cut on an angle.