I think you need to understand the definition of 3d vs 2.5d, if you are using a 3-axis CNC, then you will only be able to do 2.5d or relief type carving like this :
to be able to do true 3d you will need either a 4th axis or you will need to slice a 3d image, cut it and then glue the pieces together like the 2nd photo.
The finished product.
I'm sure you'll get a lot of varying opinions on this but this is how I do it. Much of the process will involve the software you use, I use EnRoute pro but there are plenty of others out there. Do some searches for 3d CNC carving.
Hope this helps.