How do we keep our product private so we can patent it?

Whomever you disclose your product to, you need to have them sign a non-disclosure agreement (NDA) - an NDA effectively overrides your "disclosure" to these limited third parties - in other words, the NDA effectively preserves the fact that you have not disclosed your product publicly.

The best strategy would be to file a patent application before approaching investors. However, if this is not possible, like Steven advises, putting an NDA in place would be the next best thing. In addition, you can consider focusing on the advantages and benefits of your product and not on how your product provide these advantages and benefits to try and keep aspects of how your product works confidential during the negotiations.

In order to protect your efforts, a patent application should be filed before making it (potentially) public. Putting an NDA in place might be fine - as long as it is not broken...
A patent protects an Invention - not a particular product. You can file a patent application before you have finished your product. As time progresses more inventions may make their way into the product.
Find an experienced patent attorney who is accessible and in whom you trust. He/she can help to find a strategy that suits you best and, thereafter, prepare and file the patent application, if and when necessary.