How far do you have to dig down before you add the 2x4 and then pour

You're going to have to be a bit clearer on your question. What kind of project is this?

If you're putting wood in the ground, make sure that it's pressure treated. That way, it won't rot. As for how deep, depends on what you're doing and where you live.

If you are on Hawaii, refer to Pung61. If you are in an area that freezes, you have to dig to just below the frost line. In the Midwest that's 4 feet. I'm now in Vermont with about the same frost line but digging 4 feet when you basically live on a giant rock is interesting.

If you're on the rainy side of HI, I'd still dig down at least 2 feet or until you find firm, dry soil. You want to get below the moisture and sand.