How do you know if foods are processed or refined?

Answer 1

Something as harmless as chopped carrots counts as "processed" food, because something has been done to it (it has been chopped).
Refined foods are something altogether more complex, and refining usually means that a separation of original substances occurs, with one being discarded. Crisco or white flour are refined products, because they've been separated from other components, which were discarded.
If you are trying to avoid processed and refined foods (and good on you if that's the case!), simply buy whole fruits and veggies, whole grains, whole everything, as it was plucked from the tree. Voila.

Answer 2

White sugar is refined, so is flour. Unless it is all natural it is processed or refined.