How does one get angel investors to invest in one's company, that doesn't exist yet? what are the steps?

The official term is a "Venture Capitalist" (google it). Though Angel Investor is correct as well

If your trying to pitch an idea for a non-existent company to a potential investor you need to create a report known as a "Business Plan". This is what you present to potential investors (and banks if your trying to borrow money) in order to inform them of what your company will be about.

This is usually a pretty lengthy document because your trying to show them that you've thoroughly thought through every aspect of your company (such as who your target market will be, where your primary location will be, how much money you plan on making and the specific methods you will utilize to achieve this goal)

One thing you should try to do is show the Venture Capitalist/Angel Investor that you are investing a lot of your own resources into the project as well. No one wants to invest in a company who's owners don't have anything invested in it themselves, so if the company flops the other guy get left out in the cold and you get off "scott-free"