Only shampoo your hair, every other day. Shampooing it everyday can dry it out and cause excessive tangles which definitely isn't shiny.
You want to condition your hair everyday though, and when you do, run it over your hair like if you were to be putting your hair up into a ponytail. Also running through it with your fingers is good.
After you've applied your conditioner, use the hair comb to brush it through your hair while the conditioner is still in it, and while you're rinsing it out also comb through it.
Comb your hair again after you've dried off after your shower but DO NOT towel dry or blow dry your hair OR use a brush, all this can stress and break hair and cause knots.
Let your hair air dry and it should be tangle- free and smooth and shiny, if you don't get fast results, continue doing it until you feel a difference in the smoothness.
Side note: also, adding regular vegetable oil to your hair at the roots will help with the healthiness. I recommend rinsing it out before going out in public though as it can look greasy.
- Hair comb