In order to strike a deal with a private investor, it will be necessary to convince them of the viability of the business that you are trying to get them to invest in. If your business already exists, then you should show them documentation of your cash flow and of the general trend in how your business is doing. This will convince them that the business is a good risk. If your business does not yet exist, you will need to show them a good, detailed business plan showing that there is a true niche in the market and that your business will be able to exploit that niche.
In order to avoid problems, it is best to make a formal deal that clearly lays out the terms of the investment. It should have a payment schedule and a clear statement of what, if any, role the investor will play in any decisions that you make. In this way, you can avoid misunderstandings that can come with this sort of less institutional arrangement.