I am not the be all and end all of spont - but having failed spectacularly a number of times, I can give a few guidelines on what works.

1) Make your spont practice like a real problem. That means going over the rules, having a timer, having cards, making them pick team members, etc. The more often they do it, the less distracting it will be in competition. If you can have an outsider do it, even better.

2) Teach them how to talk to the judges. Be polite, but ask. The worst thing the judges will say is "look at the problem". And even then you can ask them what part of the problem they mean.

3) Once you do the problem, break it down.
a)Where are the points allocated? What is the most outrageous way of getting points you could do in the problem? What kept you from doing it?
b)How was your teamwork? Was everybody included? Did you have any conflicts? How were they resolved?
c)Verbal: what was your best answer? How could you make it better? Did you have 2 or 3 answers in reserve?

4) Help the team figure out what everybody's role is. Who can read along with the problem and keep everybody on track? Who is good at logic? who is good at building? Who is good at using materials in creative (and effective) ways? Who will do what they are told? (an undervalued skill at times).

5) Plan strategies that can be used in the future. Let's say you have to communicate non-verbally - if you have a strategy in place, it makes implementation that much easier. For verbal problems, practice things like alliteration, rhyming, and storytelling. Make a non-verbal signal that the #1 person can use to start it off. Learn the basic storytelling themes, then how can you change them to be surprising?
Origami can be helpful in hands on situations. For construction, learn the basic shapes that work. Triangles are more stable than rectangles. Marshmallows are an effective glue. Pasta can be glued together, but you need to start applying spit right away.

My kids have always found spans easier than height. I'm just sayin'

6) Realize that your materials and conditions may not be ideal. It's not a bad idea to give your kids substandard materials - less-than-sticky labels, odd size sheets, etc. When they say "But this doesn't..." ignore them. Fact of the matter is that the poor judges put together this stuff right before the competition, and what's there is there. Better to deal with what you have than complain about how it should be.

And good luck to all of you! If you have strategies that work, serious (or not serious) disagreements with what I put up, post it!