This is terrible advice. When teeth are removed, the bone of the jaw has to remodel, which takes months. If you get fitted for dentures right after your teeth are removed your dentures will fit poorly. A good dentist will offer you a temporary denture that is cheap and of lower quality material while your bone is re-modelling then after a few months they'll make a high quality set that will fit much better.
Not really overnight thing though, right? Its painless and long procedure. Never heard of this being something that can be done within day or two (complete procedure).
There are cheap places that offer dentures in a day, or a few days but you wouldn't want to go to one of these places. When your teeth are pulled your bone has to remodel which takes several months. This guarantees that dentures done shortly after getting your teeth pulled will not fit.
Generally, the dentist will take a preliminary impression, that is used to make a custom tray. This custom tray is used to make a final impression. Then the dentist will make rims that shows the lab where the teeth should go. The lab uses the final impression plus the rims to make a wax try-in that has teeth so the dentist can make sure the teeth are where they are on the denture and the patient approves. Once the wax try-in is adjusted by the dentist, the lab takes it and makes the actual denture for the patient. It generally takes several appointments.
But yeah, like the other comments have noted, this probably isn't very wise. I didn't mean to offer real advice, just say that it's essentially possible, with tons of pain and considerable amount of money.
In the end, you probably just want to hold on to those natural teeth.
If you are serious about it though and you want a reasonable price, take a trip overseas and have it done there.