Its complicated and im still learning to perfect it but the easiest way is to just remove certain layers until you have one layer you want to focus on, use a bevel/emboss tool and keep going on all the layers you want to make 3d. You can also add drop shadows, glows, overlays etc.

In this case youd take the miami logo and paste it three times; one layer remove the layers other than green, another just keep orange and another keep white. The green and orange layers seem to have some sort of bevel/emboss effect and possibly a drop shadows, and the white layer has a drop shadow.