While very few of us can say their job depends on giving speeches to the general public every day, it is fair to say that in most jobs, from time to time, you will need to give a talk, presentation, or weigh in on an important discussion. If you work for a large multi-national of some type, you'll be familiar with the numerous conference calls held between global regions and departments. These days video conferencing can be done at your desk, either with a networked desk phone or webcam. Anyway the point I'm trying to make is that even when you don't really think of your regular meeting as a public speaking exercise, it really is, and the better you are at directing your thoughts effectively while not being too nervous, the more opportunities there are to be noticed and considered for other projects/roles.
Useless tips I've received from other people on how to do better at public speaking...
"Get a good night's rest before the big day" -- Laughable. If it's important (just like an important exam) you won't be sleeping that well. Just accept it and try to get a few good hours. No one will be surprised if you look tired.
"Ground yourself" -- this might work for some people, but if you are terrified of public speaking then there are better ways to deal with that anxiety.
"Imagine everyone naked" -- no, just no. The only thing you should be thinking about is what you're saying.
Tips
Practice and feedback
Rehearse the talk as many times as possible. If you are really anxious about it and you are not fed up of repeating the same words over and over then you haven't practiced it enough! For people who get really wound up about it - you need to be so sick of the material that all you want to do is go present and get it over with. In my experience, that's the best place to be at.
Preferably, give your talk to some family or friends and get feedback first, and adapt. If you are petrified of crowds, start with 1 person who definitely doesn't give a crap about it in the first place (your partner/teenager/dog/cactus) and work your way up.
Try explaining everything to yourself. Can you explain it to a 5 year old kid? If you can't explain it, you don't know it well enough yet.
Nerves
The anxiety is there for a reason: If you have practiced the material well enough, then the energy from the adrenalin gushing through your veins is generally a good thing: it will keep you on your toes, keep the neurons firing, and prepare you for doing the job.
It's practically impossible to be anxious while doing heavy exercise. If possible, exercise 2 or 3 hours before the presentation (the effect lasts). That might also help with getting to sleep the night before.
Don't take sleeping pills the night before: they are evil drugs and will stop you from thinking straight the next day. I did once, and the effects the next day were noticeable to everyone (shlurring words and slooking like you're drunk... yeah that didn't go well).
If you're one of those people who wake up at 5am with a racing heart and dreading your impending doom (presentation on the traditional diet of the wild Yak in northern Tibet, anyone?) then I recommend just getting up at that point. Cortisol peaks in the early morning to wake you up and you won't be going back to sleep - just get up.
Beta-blockers can help with panic attacks -- talk to a doctor.
Speaking
Speak slowly. Just about everyone who is nervous will speak way too quickly. SLOW DOWN and take a breath between sentences. When you're anxious it feels like an eternity going by, but it doesn't feel like that to your audience.
The power of 3. Say this slowly: The power of 3 is the most important rhetorical device because it: Has one starting point, a middle point which you may forget, and the most important ending point. People remember things in 3s, and any statement is more powerful like that. Silly humans.
Be realistic
To put it bluntly, the majority of business presentations are terrible. Speakers have difficult accents, poor microphones, and listeners are waiting for it to be over so they can do something else; therefore, don't worry so much - nobody really cares if you screw up anyway.
Think back over the past couple of years - how many presentations have you been to and you can actually remember anything about the content, at all? Zero. Nobody will remember what you say, what was on the slides, or what went badly. The only thing people tend to remember is how you made them feel.
Prepare for questions
You need to think about the likely questions and be prepared with some suitable responses. Obviously, you can't think of all the possible questions, and that's why you have to know your subject well.
I've known students to ask their friends to sit in the audience and ask pre-prepared questions. This actually works quite well as you can have them ask questions you think are likely to be raised anyway, and it helps to lower your anxiety over the unknown. There are other benefits: sometimes the audience is shy.
There's always one bastard with a tricky question. If you can't answer, be honest and say "that's a really interesting question and I'm not sure - let me find out and I will forward the answer on to everyone". If it's more of a point of view or comment on how you did something, be honest: "There's definitely more than one way to approach the project and I have shown my method is appropriate and I think it works well in this case" or "My approach was chosen so that it's easily reproducible and simple to understand, but there's more than one way to do it", etc. The secret is to first passively agree with the 'attack' and follow up with a supportive statement. Always be honest.
How to practice for real, from your desk
Okay, lets come back down to reality. Most people don't do much talking on stage -- mostly, its from their desks. That can make starting out a whole lot easier!
If you want to start doing this, put it as a goal in your "personal motivations" for the year. The secret is start small and short. For example, start setting up open-invitation meetings for giving a 'workshop' or screenshare on some problem you've been working on and keep it short - 5mins max. People love to attend short meetings which promise to explain something and then swiftly end. If you need a business reason for having the meeting in the first place, its termed "knowledge sharing".
Screenshares work great, and the most wonderful part - you can practice it by recording yourself on YouTube or whatever first. You can go over your lines and adjust things which weren't as clear as you'd like.
If this sort of format doesn't work for your place of work - I'd recommend a weekly catchup. The goal is incredibly simple: understand what people are currently working on, and whether anybody can help out. Go around the group in turn and speak about what you're up to. It can be really informal and may help in talking in front of people, even if it's your own team.
Whatever the format: You are gaining experience of speaking and talking to a group, and this is valuable for the future. When you eventually come to give a real presentation that matters, you'll already have practiced many of the skills.
This could be you - look how happy they all are! Well, except that guy at the back, he's not even looking at the presentation - what a dick.
Why bother?
If people really don't remember anything about the content of presentations (even the next day - nobody will remember much), then it begs the question why you are doing it at all. This assumes you have chosen to do it voluntarily (which may be true at work, but not for a homework assignment).
Generally, the only reason you're doing it is to shape other people's perceptions about you. Can this person put forward a good argument for doing project X? Did they explain something well? Do they have a good understanding of the problems? If YES -- they may be suitable for doing something more important, like managing a team.