Mechanism of styrene dimerization
You're right that the first step involves protonation of the terminal carbon in the  styrene double to yield a resonance stabilized benzyl carbocation.  This carbocation then adds to another styrene molecule in the exact same fashion, reacting at the terminus of the styrene double bond to again yield a resonance stabilized benzyl carbocation.  This latter carbocation then alkylates itself (like a Friedel-Crafts alkylation).  Loss of a proton from this final carbocation yields the indicated product.