The answer depends on whether the Sun has simply stopped emitting radiation from its surface or whether the core stops producing energy. In the former case we freeze pretty quickly, perhaps a day or two for lakes, rivers and the atmosphere but longer for the oceans. The atm would freeze out in stages. First there would be all the water vapour, then a frosting of CO2 and after some delay there would be the oxygen, argon and finally nitrogen. The oceans would freeze over and that would slow the cooling of the deep oceans but unless the Earth is producing enough internal heat (which I very much doubt) then the oceans would also eventually freeze solid. I suspect that the core and mantle would be unaffected and so we would still have a magnetic field (for what it's worth).
In the latter case we may not see a difference in our lifetime, perhaps not for thousands of years. The Sun has a lot of stored heat and it takes a very long time for energy from the core to reach the surface. After that either 1) we slowly freeze or 2) there is a core-collapse supernova and we fry.
One thing is certain, however; there are no good outcomes.