Tip: look for opportunities to bring ‘live’ speakers into the classroom and use them as listening practice for your students. For example, bring in to the class other teachers (in a language school), friends etc. And finally: every time that you yourself speak it is live listening, so use your teacher talking time wisely.
Listening practice via audio materials in coursebooks and on the web is fine and useful and we all do it. But an under-used resource is speakers of English who we just know as friends and acquaintances. They can be native-speakers, or good non-native speakers. All you have to do is invite them in to the class. They can speak on a pre-prepared topic if you/they want to, or your students can simply ask them improvised questions about their life/jobs/whatever.
The fact that the students can interact with them and ask clarification or follow-up questions makes the activity even more fun and useful. The students can take notes and write a summary of what they found out about the person for homework.
To give the activity more of a BE slant, the person you invite in to the class should talk about their job/profession and questions from the students should be restricted to this.
And finally: when you, the teacher, talk – it is also live listening. You can talk about something, respond naturally to questions, and then ask the learners to discuss what they understood in pairs. You could then say the same things again, but this second time ask the students to write down any useful lexis that they heard. Again, they can compare in pairs afterwards. This requires nothing in the way of materials or planning.
Here are some links to articles on ‘live listening’ all taken from a piece by Alex Case on tefl.net. They contain many activities and variations on the basic theme.