How can you be listening to another if you are busy talking?
The key to showing a person that you are listening is too not keep talking over them. They don't need to hear lots of advice at this time.
Sit back, make eye contact, nod in acknowledgement, or reflect words they are saying. This doesn't mean you never speak, but just time it carefully. If they feel you are bursting to rush in with your advice they may just not speak.
The key to showing you are giving a person a place to talk is to sit silently with their silence to give them time to reflect on what they want to say. There is nothing worse than continually asking "tell me what's wrong", "you need to tell me", "come on you can tell me". They are already in distress so emotions are causing them to get confused as it is without you adding on more pressure.
Instead say something like "I'm here for you when you are ready" and then sit quietly but attentively with them. Don't go resorting to another task while you wait, this tells them they are just burdening you and your time.
Giving them silence and space allows them to calm the emotions and enables them to find words to share with you.
Maybe ask a friend to try this with you and see how it feels.