Serums are a good way of getting shiny hair, yes. I have a serum for dry hair from Ducray, nice stuff, smells good, sunscreen included, and smooth, nourished hair.
To me a shiny hair is a healthy one, which means i take care of my hair, not overly oily roots, nourished lengths (especially if you have long hair, long dry hair looks awful!). You can finish rinsing your hair with cold water, and use a conditioner, it sounds basic but it helps making your lengths look more polished and shiny. Invest in a brush with natural bristles, it's softer on the hair and a gentle hairbrushing also adds shine.