how to connect iphone se to car radio auxiliary port

You'll need a 3.5mm stereo cable.

https://www.amazon.com/Parts-Express-3-5mm-Stereo-Cable/dp/B002T4OMG8

Just plug it into the headphone port on the iPhone and the other end to the Auxiliary port on your stereo. Follow the instructions for your stereo to set the input to the auxiliary port.

So what exactly happens? Does the audio keep playing through the iPhone speakers?

Do you get no audio at all?

Are you sure you've pushed the cable completely into the headphone jack on the iPhone. you may need to apply a bit of pressure to get it to go all the way in.

Follow the instructions from the support link you posted from > Get help connecting your iPhone, iPad, or iPod touch with your car stereo - Apple Support