There is a direct correlation between attentiveness and good listening. The more attentive you can be toward the person speaking to you, the better listener you will be.
But how exactly can one "be attentive"?
I've been going on and on about body language lately, so no surprise I start here, but the first way you can show your (listening) partner than you're attentive is with your body. Make eye contact, keep your posture open and inviting, use small movements like head nods or tilt to encourage them. Never turn your body (or even point your toes!) in a different direction. Don't look over your shoulder. Don't pull out the phone.
Be absolutely, 100% physically present with them in the moment. No darting off. No interruptions. Stay. Put.
Since I've sprained the ankle, I haven't been to yoga in a few weeks. But I know when I finally do get to go back, one of the first things they'll say at the start of class will be "bring yourself to the mat; you've brought your body, now bring your mind".
Attentiveness is about being present. Having the correct intention. So when you start thinking about all the things you need to do (work, money, kids, chores, etc.) or other distractions tug at your mind, you have to let all that go and return your attention to the person speaking to you.
Remaining mentally focused on the speaker makes a difference between clear communication and missed important information. And if you've found that you've wandered, or missed something, politely ask them to repeat themselves: "Oh that is really interesting. Let me make sure I understand that..."
There is a difference between empathy and sympathy. Be an empathic listener (understanding). Not a sympathetic one (patronizing). Try to put yourself in the other person's shoes, adopting their stance and facial features to see how they feel. Don't superimpose your experience on them in any way. No "if I was them/if I was you..." Don't come to the conversation with an attitude like "whew as soon as she shuts up about her problems, I'm going to tell her all about mine." No topping. No advice giving. Just be present and feel what they feel, sharing the moment. Try to leave your own feelings and prejudices out of it.
Easier said than done, I know! :D