What do we do if SETI is successful?

Send memes. Most commenters here assume receiving a message means aliens can reach us - they can't. Think about how distant the closest galaxy is and think about how long it would take to reach them even at light speed. The size of the ship needed, the amount of fuel needed not only for acceleration but stopping as well. Even if they 100x or 1000x our space abilities, it would still be impossible.

It also assumes that it is nearby aliens. Our radio transmissions have only gone 100 light years, and probably not detectable beyond a few. But the aliens could be saying hello to everyone from thousand light years away.

It also could not be a message. I think we have ruled out nearby Dyson Swarm (as in thousands of light years), but we could find one in rest of our galaxy or even Andromeda. Dyson Swarms should be noticeably weird infrared stars.

It is also quite possible that we never decode their message. Even with one designed to be decoded, their thinking could be too different.

Or they could just pop up here because they have mastered quantum physics and can just use quantum tunnelling to teleport whole ship across space in an instant.