Just keep introducing them. Encourage him or her to take a bit. Show off and make a big deal about you or SO/DH or older sibling eating "the new food". Make sure you exagerate "just one bite" or "just a taste" or whatever term you decide to use.
I personally dont let my children down from the table until they've taken at least 3 bites of "the new food" ...but many parents look down on that. Works for me. My boys are now 3 1/2 and 4 1/2 and it is no longer an issue.
My daughter isn't really picky. I think there are only a couple things she doesn't like to eat. I think it has to do with me breast feeding (since breast milk tastes like the food mom eats) and not giving her bland jarred food.
with my daughter, she loves strawberries so i tell her for each bite of a new food she takes she can have a strawberry. both things are healthy for her and as long as she tries it i'm fine. if she tries it and really doesn't like it than that is fine, but usually she'll try it and get this shocked look on her face when she realizes she likes it.
2 is old enough to be eating with the rest of the family. Prepare meals loaded with fruits, vegetables, whole grains and beans.
We have the 3 bite rule; everyone tries three bites, and if they don't like it they have whole grain toast with peanutbutter and honey with an apple (even my husband does this sometimes).