1. Make it visible
If your guests can't see who's speaking, they will start to talk. Make sure your stage is raised high, or improvise if there isn't one. At the launch of Social Diary 7 years ago I slipped my shoes off and stood on a table to give my speech - they saw me!
2. Make it LOUD
If people have to strain to hear they will also start to talk. Test the equipment before the event, and understand that when the room is at capacity the sound will need to be higher. Have someone stand at the very back when the speech commences to give a hand signal to the sound desk if the volume needs to go up.
3. Do it early
What happens to YOU when you've had a few drinks...you get chatty, right? Get the speech element of your event done & dusted before people are onto their 4th drink when nothin' will keep them quiet.
4. Choose your speakers wisely
This is crucial. If your speaker is not experienced, consider giving the job to someone else. If a CEO has to speak but is likely to lull your guests into a slumber, give them a minute & a half maximum, or better yet - have them simply introduce a more qualified speaker or get them to call a toast. Bad speakers can make people snooze, cringe or worse: leave. Great speakers engage, humour and dazzle. Fabulous speakers do all this without notes. I am a huge fan of the paperless speech. I'd rather someone orate from the heart than read word for word from an A4 page.
5. Adhere to The 10 Minute Rule
Speeches at a cocktail party should be under 10 minutes - maximum. Say the word speech and most people roll their eyes, but it doesn't have to be that way. Speeches can enhance an event, give it purpose, explain a concept, and delight your guests. Never moreso when they are short & sweet. Don't forget that at a cocktail event people are on their feet, they've come from work and most importantly, they're drinking. Keep the long drawn out tomes to sit-down scenarios and seminars.
6. Position your army
When I was at the event mentioned earlier, I wondered how the constant chat could be avoided when they had several things stacked against them: there was no stage so most people couldn't see the speaker, the sound was too low, and the speeches had started too late hence people were boozy. The solution? Position your army (well, about 3 people) at key spots towards the back of the room and in the corners, and have them face the people in that area with their backs to the speaker. People are very unlikely to talk if someone in authority is glaring at them, ready to say SHOOSH as soon as they do. Try it.
And if you've put all these tips into action and people still won't shut up, then aim a speech-jamming gun at them. Yes, these 'guns' are real. That'll learn 'em...