Cheapest way is generally to capitalize on someone elses loss by purchasing a partial built car.
Then buying an older completed car can save dollars, not many manage to build them for less than resale value (although market is heading south as far as used Cobras go, prices seem cheaper than a few years ago).
Building from a new kit, as others have said, most of us purchased the kit, then assembled it as money and parts became available. I always viewed my car as a "toy" rather than a must have, so only bought stuff when i truly had the money spare.
From my kit purchase to compliance inspection was almost 6 years, so as long as you have patience then it can be done without being a burdon.
A longer build time also gives you a chance to hunt and find the bargains, I purchased a few parts from other builders as they upgraded there own cars, I also am very hands on and did all my car apart from side pipes and main body electrical harness.
My build is far from a "pretty car" but it is what I wanted to build.
I am at a hair over $40k as my car sits.
(Here is a pic as I love seeing my car)