Thanks a lot for your suggestion! I agree with you that this will help me in a long run for my programming skills. However, what I'm actually looking for is experience at running a business/startup.
You won't be able to learn too much in 3 days, and also none of the guys at a startup will take a lot of interest making you understand things considering the short tenure.
Pick up a small idea - some pain point that you see in your daily workflow. There are so many possibilities with free infrastructure today, Heroku, Google App Engine, and of course Amazon WebServices.
Start contacting people to see if they are interested and go through the proper way how someone seeds a startup. This will help you learn something that no experience ever will.
I believe 3 days is enough. A new marketing idea can be implemented in 3 days; a new UI mockup can be done in 3 days. To me, I'll be learning things, but to the founders they can actually benefit from my ideas or executions. It's free after all, and they can definitely take it further after the 3 days (maybe hire me something).
I assume when one says for 3 days, he/she knows that they won't have time after that - or else, they would have agreed for a week/two or so on. What if the idea/mockup was not completed in 3 days, and the trainee was not willing to spend more time...
From a founder's perspective they lost the time. Probably for mitigation they would have someone else implement the idea too... which would indicate that they might not provide the same attention to your implementation.
Start a startup. Pick a little idea, build it, market it and see what happens. You'd probably learn a ton more that way than working remotely for 3 days.
