"What's the best way to handle a junior coworker who acts disrespectfully or oversteps in meetings?"
If you're the manager, call the person into your office later that day. Wait a couple of hours so it's not obvious to everyone else who was in the meeting. You need to be clear, but of course address the issue in a way that's comfortable for you. I tend to be frank. I've come right out and said, "Explain to me why you handled the situation in the meeting that way." Or, "Jamie, I was very uncomfortable with the way you handled that, and I found it borderline rude. Maybe you can tell me what's going on." People usually open up, and it all comes out. There's a good chance it's about something else entirely. So have the tissues ready.
"How do you deal with a junior coworker who cries at the drop of a hat?"
Let it happen a couple of times to make sure it's a trend. Then, when everything's fine, talk to her. Keep the mood light. You could say, "Please take this in the spirit in which it's given—as a coaching moment. I've noticed at times you cry when the situation doesn't warrant it." Tell her she can excuse herself next time. (The phrase "I'm having a moment" could help.) And she can return once she has collected herself. If it's a peer who's quick with the waterworks, handle it with humor and help her laugh it off: "Are you kidding? This isn't worth the tears. It's not neurosurgery." (Note: If she is a neurosurgeon, she's on her own.)
"How can you best manage an underling who's also your friend?"
You've got to be careful, because others may have the perception that your friend is getting preferential treatment or is privy to confidential information, even if this is not the case. I personally am friendly with everyone on my team, but I'm not friends with anyone on my team. That works for me. If you've just been promoted out of your peer set into a new role, it might make sense to have a frank conversation to lay the groundwork. Let the dust settle, get into the job, and then say to your friend, "This is awkward. But as you know, there will be times when I'm not going to be able to share everything with you. Our friendship means a lot to me, so I hope you understand." Honesty is your best tool here.
"What's a "good" way to fire someone?"
If you need to fire someone because of restructuring, be calm and professional and direct: "You've done great work, I respect you, I will give you a reference, but unfortunately the company is being reorganized." If you're firing someone due to poor job performance, make sure you've started the communication ahead of time. I'm not a huge fan of a formal first-warning, second-warning process, but you should be discussing problems as they occur. When the time comes, you can say, "It's no surprise, because you and I have had several conversations about what's working with your job performance and what isn't working. Unfortunately I haven't seen the kind of improvement we need from you to help us hit our goals, and I'm going to have to let you go." It's better to do it earlier in the week. Then people have the opportunity to network right away—make calls, set up lunches—rather than just go home and have a terrible weekend.