Presenting work-in-progress (slides now available)
It sounds from your question (the use of the word 'willing') that one deterrent is the unwillingness of students to present. Since it's in your research group, I'm assuming that being scooped is not something they need to worry about :). So the real reason is that they feel afraid: of seeming clueless, of not knowing the answer and having someone else find it in 5 minutes after they start presenting, or of people deeming their ideas to be uninteresting. 

In other words, the imposter syndrome. 

One of the most important transitions a grad student has to go through is the point when they realize that they can actually play in the research world, and make contributions of their own. This often comes when their first paper gets published, but can also happen the first time they talk to a "senior" researcher and realize they know more than that person about their topic of interest, or even the first time they prove a brand new result. 

One advice for you might be to give such talks of your own, where you show "how the sausage is made" and show how ill-formed your own initial ideas might be. That gives them a model to work with. At the very least, you can give them examples of the winding path a research project takes. 

A second advice you can give them is to remember that most likely no one knows as much about their problem as they do. They may not internalize this just yet, but repeated reminders might help :)

When they actually give the talk, Sylvain's advice is very good: however I don't think the 1/3 rule applies here since in your research group there are probably no outside experts and probably no generic audience. But I'll mention a line I heard yesterday in the context of journalism, but which applies very well for talks by inexperienced people:


  Don't overestimate the audience
  knowledge, and don't underestimate
  their intelligence.


In other words, provide all the background they need, and more. But don't prove teeny little lemmas from scratch.