If you have a friend who's going through a rough time, offer to talk about it with them over a coffee. Think of all the times you've wished you had a friend to talk to--be proactive and be that friend for someone else.
Simply listening will show how much you care; your friend knows you are busy too so the fact that you are setting aside time to sit and listen to them can really mean a lot.
As you take the time to listen to your friends and family you will get to know them better. You will discover their passions, their fears, their hopes and dreams. Over time you can help them accomplish these things, too, but the first step is always listening. When we take the time to listen to others we take our focus off of ourselves, and that is always a good thing.
Offer to meet weekly with a friend in your life who is going through a particularly hard and difficult time. Perhaps you know someone who is getting a divorce, or who just lost a parent. Perhaps you have friends who are back in school for the first time in fifteen years and they could use someone to talk to. Pay attention to the needs of your friends; if it seems they have a long journey ahead offer to meet with them each week. Let them know that you simply want to listen. You can make it a regular coffee date or just let them call you whenever they need someone, even if it's two o'clock in the morning! While your friend is sharing, don't advice unless they specifically ask for it. As hard as it may be don't try to solve their problems for them, and instead simply listen to what they have to say.
Listening to someone doesn't have to be a long commitment. And sometimes it can even be done over email! Maybe you notice one of your coworkers seems to be a bit down; stop by their office and invite them to lunch. Or maybe a friend or sibling is more quiet than usual; ask them if everything is alright. Sometimes we don't even realize we need to talk to someone until we're asked.
Some tips on how to be an effective listener.
How good of a listener are you? See if you are already using these techniques as you listen to your friends.