[SS Engine Guy]

Easy answer. Start out being a "gear head" at age 12. Haul water and wash cars/ramp trucks and do all the tasks that your "heros" don't or won't do. Work butt off for 40 years in machine shop. Eat, sleep, breath horsepower. Learn how to do your own stuff because you learn the hard way that sometimes nice expensive race motors and trans are built out of someone else's used parts. Work 14-16 hour days at least 6 days a week. Vacation consists of going to races. Bottom line: learn how to do as much of your work as possible and develop the theory that nobody can do it as well as you because you will spend any amount of time it takes to get it "right" and make sure all the details add up. As you are learning, surround yourself with the "best" people in drag racing, whether it is a manufacturer/supplier, an employee or just beer drinking buddies. Don't ever pay an entry fee at a racetrack that when you pull thru the gate you aren't sure that you have a better chance than anybody there to win. (winning attitude). Along the way you will find out that some of your heros were actually more BS than action. If you ever feel like "doing it the easy way" quit racing.
Somewhere along the way you will find that you have collected the knowledge and skill to do things that you didn't think you ever could do. And by doing this for many years you will have become successful in business also. Hopefully by this time, you won't be burnt out or have ruined your health. If you aren't healthy all the rest dosen't matter. Try to encourage and help those who ask for it or that you think need help whether it is on their race car or their lawn mower.
This is just my experience. This is how I afford my racing hobby. I started out with street cars bought with lawn mowing money, advanced to worn out tow trucks and flatbed trailers, changed valve springs on the flat trailer at 3 in the morning with a light bulb in order to be at the track after a 8 hour drive and try to get teched. Slept in cars in the tech line at malls. I guess that is what they are talking about "paying your dues".
I also want to mention that I had a Great Man for a Father. My Dad didn't care much for race cars but he always taught me the skills that he knew, developed thru a carrer in the Army and many years in business after that. He was always there to give advice and his opinion if I asked for it.

Racing, or any competition, can be the biggest reward or source of satisfaction that there is. And some have it easier than others I guess. But if this is what you want to do and you intend to be successful in it I don't see any other way to do it than the ways I have outlined. The late Bill Jenkins, John Lingenfelter, Lee Sheperd to name a few, and many, many more still with us, did it this way.

I guess I really didn't answer the original posters question so I'm going to try to.
Some that can afford these new cars or just a really nice, quick S/SS are successful businessmen and owners of companies, some like myself, have just worked around racing for years and made decent money, some can get great sponsor deals, some are into illegal activities, some are outright crooks, some, like Julie said, spend money recklessly, some spend their retirements or morgage property, some have at some point held really good jobs with good pay, maybe some won a lottery, etc. etc.
As in other things in life, you spend what you know you can afford. I don't suggest borrowing money to go racing. I am as impressed when I see a well thought out "dime rocket" as I am a state of the art piece. Those who know how to really work these drag cars see things different than the average "car guy". I laugh at front end geometry so far out on a 200k car that it shouldn't be allowed to race. And I marvel at the slower stocker that you can push thru tech with one hand. I guess, starting out at an age of maybe 30 I would suggest buying a known good car at the track as was mentioned. But I would get to know that car inside and out before I put much thought in racing it. I have seen too many people buy a fast piece, race it for a couple of races, break it and never be fast again. Mainly because the previous owner knew how to not only build and race a fast S/SS but also knew how to fix it. Not too many got to start at the top as several of these posts have pointed out.

As was said earlier. Add in your entry, traveling, routine maintenence, testing costs into your racing budget. With todays artificially inflated prices, this alone can get really expensive. It is actually crazy the amount of costs just to pull into a race these days, vs. the payout both from santioning bodies and most manufacturers. I have had customers, a few years ago, that actually made some money chasing points and some that broke pretty close to even, however, the "touring" guys are having a hard time breaking even with rising costs and shrinking payouts/contingencys as is common in our sport today.