How do you approach a programming project from conception through code?

Say you are hanging out with a fellow developer one day and the two of you come up with a really cool application idea that could be useful to a lot of people.... Something that is definitely a medium to large-sized application project.

What hard, tangible steps do you take from that point on as soon as you get back home?

Do you research to see if the idea already exists? If it does, do you investigate or perhaps download the existing application and find its weak and strong points?

Do you open up a Word document and start jotting down notes?

Do you begin coding without fully understanding what it is that is needed?

What do you do if there is a specific area of the program that is required that you have never dealt with before? Do you create a small program just to learn that area?

Walk us through your process of investigating a problem, finding a conceptual solution, and then transmitting that into a software application. Try to specify timeframes as well.