How to design 3D logos like this?
You can render a 3-D image using 3-D rendering and modeling software, or you can draw a 2-D image that looks 3-D. (or, in many cases, a bit of both)
The left logo appears to be modelled, the right logo appears to be a 2-D illustration.
To do 3-D modeling, you'll need to get some 3-D software and learn it. Options include SolidWorks, SketchUp, Maya, and many, many others.
To do 2-D illustration that looks 3-D, you'll need to learn some basic illustration skills (perpective, shading, scale, etc.) and then learn some software to draw it. Options include PhotoShop, Illustrator, InkScape, The GIMP, and many, many others.