It is difficult to describe a hot-rod without showing some form of emotion. Perhaps you should watch and listen to the music in the first video below, just to get in the mood. And the translation of (iron) 'rod' doesn't appear to help a great deal.
To cut a long story short: First of all, it's the body of a genuine old-timer, preferably from the 1930s, combined with a powerful engine. Due to the fact that this type of engine wasn't even available at the time, the best thing to do is to use the entire drive train including the rear axle.
Of course, generally the car is made wider. It would appear, that in the USA, anything goes, that means, if the mudguards are left out, almost any (rigid) axle will be able to be fitted. Now of course, the front axle is narrower. Once again, in reference to the USA, it's left like that. In Europe, the car would not be given a roadworthy certificate.
It's hardly possible to get hold of rigid front axles, which fit to the rear axles, because cars with powerful V8-engines needed independent suspension, at least in the front. What remains, is a pretty complicated modification to the front-end independent suspension. What one needs, is an axle with a cross member, which is welded to the chassis or replaces parts of it.
As you can see, there are at least two types of hot-rods. In one of them, the mechanical side is left alone, except for the engine and the (automatic-) gearbox, thus taking a chance with the old final drive. The others are comprehensively modified, in fact it's only the coachwork and sometimes the interior, that distinguishes them from more modern cars.
Of course, the super structure is not ignored either. Although often very box-shaped, the body-work is chopped down so low, that inside the car more length is needed. This is why old coupés are particularly suitable, because their B-pillars are shifted further to the rear. Sometimes, as you can see in the second video below, the driver even sits on the back seat.
Don't be fooled, not all American hot-rods have to be in a miserable condition. There are examples which are complete with modern suspensions and even with disc-brakes, which, when such a powerful engine is used, should actually go without saying. Then of course, the amount of financial investment differs considerably.
In this case, the rust is not simply treated with clear varnish, but a special spray-job is on the cards, the paints, e.g., those with metal-flake, are so expensive, that it's wise to leave the spray-job to a specialist. Indeed then, prices of €5,000 to nearly €10,000 are quite possible.
Once one has got to this stage, nothing more stands in the way of the individual interior composition. This is of course, good business, e.g., for the saddlers, who are pleased to do the fine leather work. The rest of the money is swallowed up by, e.g., the self-designed rims and the various requirements necessary for the registration of the car.
In this respect, the Americans are streets ahead of us in Europe, because there, the (somewhat wealthier) kids can probably afford to have hot-rods. However, based on the enormous safety deficiencies, any sort of tolerance is uncalled for. 12/13