For my first and longest tour, I'd saved up 8 weeks of vacation, and took the rest as leave without pay. That was the summer my youngest daughter and wife graduated college, three months after we paid off the mortgage, so finances weren't such a huge worry.
If you have money but little time, you can afford to travel to different areas of the country for a week or two. If you have time but little money, you can camp and cook, ride and live cheaply to see large areas. If you don't have much of either, find someplace local where you'd like to ride for five days to a week, and get rolling!
I'd started commuting by bike four years earlier, so I had a bike and one set of panniers. That saved and average of $75 a month in gas and wear and tear on the car, which helped finance the other set of panniers. Once you've got camping gear (which I already had), it's good for a very long time.