No additional smog parts will be needed. Simply visit a California smog check station and ask for a smog check for the purpose of initial California vehicle registration. The smog inspection for late model vehicles (OBD-II) are fairly similar to other states. Just make sure your check engine light is not illuminated and your Toyota Solara's battery was not recently disconnected or needed charging. Part of the smog inspection will check that the emission monitors (also known as Readiness Flags) are ready.
The rule is a USED vehicle is eligible for California registration even if its emissions system is only 49-state legal (Federal Emissions) as long as it passes an emissions inspection at a California smog station.
