It would help if I knew a little more about the logo. There is no way to extrude shaped directly in After Effects, but you can stack up layers in Z to fake depth, use Shatter to fake extrusion, use 3rd part plug-ins like Zaxwerks to create 3D objects with depth, or create your 3D logo in a 3D app (Blender is free) and import that animation into AE.
Show us the logo give us a description of what you want to do with it and we can help more.
AE works natively only in 2.5D space - moves 2D layers in 3D space, so no extrusions, displacements, shapes, modelling, etc. There are a few plug-ins that can give your layers 3D volume (like ShapeShifter AE or FreeForm PRO from mettle.com). The modelling part is quite limited, but if you're not doing anything very complex, it should do.
Here's an article that gives a good summary of the various ways to extrude graphics into 3D using After Effects:
In many cases, it's easier to do the 3D work in a 3D application and bring the result into After Effects for compositing.