There are three options: bus, train, and plane. Buses are the cheapest, but it's a pretty long bus ride because you have to go around a fair amount of water. Same thing with the train--the express train is finally back in service, but it's still a long haul. Planes are surprisingly cheap and fast--it's less than an hour to Izmir. Check Onur Air, and I think Pegasus may also run that route.
If you stay in Selcuk overnight--and you should, it'll save you quite a bit over a comparable place in Istanbul, many of the B and Bs there will pick you up at the airport for a reasonable fee and then shuttle you to Ephesus.