Dehydrohalogenation removes the halogen and the attached carbon forms a double bond with another carbon. But then hydrogenation of this double bond into a single bond is spontaneous (it just needs a catalyst to speed up).
Pretty much. Yes, it's going to be two separate reactions. Next, you need to reduce the double bond somehow, as by catalytic hydrogenation: i.e., high pressure H2 + a suitable transition metal (Ni, Pd, Pt, Rh, etc).