Start-ups are inherently risky. For this reason,I would not consider one unless I had at least 3 months of income saved and preferably 6 months to a year. I've known too many people through the years that were having a great time at a wonderful start-up that stopped paying their paychecks very abruptly with no clue that the company was about to be out of money.
To reduce the risk (and start-ups can be a great place to expand your skills and lots of fun to work at so you may want to work there even with the risk) - I would consider some of the following:
How much of their idea are they willing to tell you. From what they told you does it sound like something that would have a viable income stream? If it is a consumer type product, would someone non-technical be interested in purchasing? Is is going to depend on ad sales or customer payment. Do they have an actual business plan that they will share with you after you sign a non-disclosure agreement. Start-ups without things like formal business plans are much more risky. This tends to mean that the money source is not professional (or really non-existant, most places that lend money to start-ups insist on a business plan) which is usually a bad sign.
What track record does the current top guy have? It's alot less risky to work on a start-up run by someone with a track record of running another successful business. If the start-up has no one with business-running experience at all - run like the wind. Are they hiring marketing people as well as developers? A great product that no one knows how to market will still likely fail.
Are they spending their intial funding on nice-to-haves or must-haves? Those with the fancy offices with the fireplace and the entertainment room, etc. are the ones most likely to fail. Nice-to-haves come after the income starts coming in, not before.
If you are not willing to move, are there other places locally that you will be able to get a job in on short notice if they fail. If the area has plenty of development jobs, you can probably afford to take the risk becasue you won't be out of work long if the company fails.
Are they going to expect you to work 80-120 hours a week for almost no pay for the hope that you will strike it rich in the end with your stock options? Assume that the stock options will be worthless when deciding if the salary and work conditions are acceptable. Don't bet on an outcome that is not likely.