While there is always more to be said, there is an entire FAQ section dedicated to Nazi Economics and the German rearmament. I suggest starting there and if you still have questions, feel free to ask more specific questions.

If you want a very brief TL;DR then here it goes: They financed it using every dirty trick in the Big Book of Economics and some so dirty that they had to invent them. During the later parts of the rearmament the German economy was constantly balancing on the brink of collapse. By 1938-1939 Germany was very much all-in. The only options available to Germany was an aggressive war of expansion or total economic collapse. They also creatively violated almost every stipulation in the Treaty of Versailles through various creative loopholes. So, in conclusion, they did it by largely ignoring the treaty of versailles.