Assuming that this is the roof mounted BlueConnect unit, it really should be as simple as pressing the phone button, and then saying "set up", and following the prompts.
There is an outside chance that you have a defective BlueConnect unit, but the fact that you got the prompt once would indicate that it is working at least somewhat normally.
Make sure that you conduct the setup with the car parked, and the windows up, while seated in the same position that you would be for driving. Make sure that electrical system is at least in the accessory on mode, or that the car is idling (on).
Also, don't get hung up on the blue light - you will normally only see that while you are actually on a call, and in my experience (not on the Genesis, but other cars with the same system) the light is often not all that visible except at night anyway.
One final thought - turn your phone off, first, and try to get the BlueConnect into phone pairing mode. This will allow you to rule out any odd behavior on your phone's part as being related to the problem. If you get the BlueConnect into pairing mode, you can always turn your phone on again, and then continue pairing as normal.
Good luck!
Here are the instructions from the standard manual:
1. Press and release the BlueConnect® PHONE button and say "Set Up".
For example, say, "Set Up" at the Main menu and BlueConnect® prompts
"Select one of the following: phone pairing, confirmation prompts, select
phone or say cancel to return to the main menu." If there is no response to
the prompts, BlueConnect® reminds you of the selection two more times
until you select an option. If there is no option selected after two repeats,
BlueConnect® will power down.
2. Say, "Phone Pairing."
3. After the system prompts you, say “Pair a Phone.” The system will remind
you that pairing should only be completed while the vehicle is in park.
When the vehicle is in park say "Continue."
4. The system will then ask you for a 4-digit PIN. This can be any number you
choose as long as you enter the same number on the phone later.
Say your four-digit PIN. For example: "One-Two-Three-Four"
5. Follow your cell phone manufacturer's instructions for placing your cell
phone in a pairing mode.
6. Select BlueConnect® on the phone. Then, on the phone's numeric keypad,
enter the same PIN number as entered in step 4.
7. BlueConnect® will prompt you for a phone name. Name it something easy
to remember. Say the phone name, for example, "Jacob's phone.”
8. To complete the pairing process, BlueConnect® will now ask you for a
phone priority from 1 to 7. Number 1 is the highest priority. If two phones
are paired, BlueConnect® will use the higher priority phone when both
phones are within range. Say the phone priority, for example, "One."
9. When complete, BlueConnect® will indicate "Pairing Complete.”