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Mumbled, rushed, and chaotic points can't be accurately communicated. If you want to prove a point, slow down and speak it confidently, and don't stop until you're finished making your point. People tend to listen more closely if you slow down and speak in an even, measured tone, rather than quickly rush over your words as if nervous. If you're in a big group discussion and are struggling to be heard, cut yourself a chunk of air-time by grabbing the floor and then slowing down the back-and-forth. Say, "I'd like to say something" and then pause for a beat. Take a breath before continuing. Once you've got the floor, you've got the floor for however long it takes you to make your point. Make everyone hear you. If people sense lots of emotion or hesitancy in your voice, they may not take you seriously. Anger or snobbery in your tone also causes people to get defensive or tune you out, rather than listen closely. Speak calmly, even when giving someone bad news or disagreeing with the boss. Give other people the benefit of hearing your true thoughts and feelings. Trying to be "friendly" by hedging your points, or hemming and hawing, will undercut the good points you're trying to make and only give people reasons to doubt them. Let a clear head prevail and take a deep breath before you need to make a contentious point. Introduce your point by saying, "This may not be popular, but here's what I'm thinking." This suggests that you've got the good of everyone at heart, rather than trying to be provocative or dissent for the fun of it. Package your point as just that: an idea that you have, which is perfectly valid to disagree with. If you're going to say something contentious, keep it focused on yourself, using the word "I" as opposed to lashing out at someone else. For example, you shouldn't say "Your music is too loud," which is confrontational and unproductive. Instead, say something like, "It'd be helpful for it to be a little quieter in here so I can finish this project. Would it be ok to turn it down for a bit?" Big difference. Reasoning is important when you're trying to make a point, but it's also important to focus not only on why it is you think your point is valid, but how that point or idea will help reach some larger goal. Points need context more than they need complicated reasons. For example, it may be a valid point that the music your office mate is playing is "too loud," by quoting decibel statistics, talking about hearing loss as a result of listening to loud rock music. However valid, these may not be the best way of getting your point across. Stay focused on how the music is distracting you from doing your job, the goal of the work day, not on your office mate's hearing. The best points are concise. Cut out all the hedging and learn to recognize when your point has been made. It's common to use too much packaging, when it's usually better to just cut to the heart of the matter, make your point as simply as possible, and then hash it out. If you tend toward making points that sound like this: "So, it might just be my own personal opinion, because I'm pretty new here and less experience than everybody else, so feel totally free to correct me if I'm wrong, but I was just noticing that it seems like maybe we could possibly use less paper in the office?" try cutting straight to the point and speaking more authoritatively. "I noticed we use a lot of paper in the office, five reams a day. Have we talked about cutting back before?" Lots of people talk too long, repeating the point that's already been made. If you tend toward this, just stop talking. Embrace the silence. Pausing after you've delivered your message gives your idea a chance to sink in, and also gives you time to regroup and organize your thoughts. Practice hitting pause, then putting on a calm face. After you've made your point, stop talking and listen to what other people have to say. It's not your job to immediately launch into a defense of your point, or package it like an argument. Just sit calmly and let the other people or the other person respond, listening closely. The less protest you put into it, the more likely the others will be to agree. It's very important to listen actively in a discussion. A good way for a chat to turn into an argument is to stay focused on what you're going to say next, rather than actually hearing the other person out. Don't worry about forming a response until you've really listened to and processed the other person's thoughts. Respond calmly to their points if you need to. Allow yourself to be swayed as well, and use the conversation as an opportunity to deepen your collective ideas and form a new plan or a new point together. Collaborate. To try to get your point across, lead with your biggest and best reasoning, tell the person once, and then let it go. Getting sucked into a petty argument with someone who just wants to bicker isn't a productive use of your time. Once you've put your point out there, you shouldn't try to make the same point with weaker evidence, or allow someone else to wear you down with pettiness. Just learn to let it go and give the other person a chance to mull over it.

Summary:
Speak slowly and clearly. Keep your voice calm and friendly, but firm. Use "I" statements so the other person doesn't feel attacked. Explain your goals. Be brief. Listen to the other person. Learn when to let it go.