I'm going to show you how to take a 2D logo and make it into a 3D one using SketchUp.
Step 1: SketchUp and Plugins
From there you will need to download a plugin called SketchUp STL from this site http://extensions.sketchup.com/en/content/sketchup-stl.
To install this plugin launch SketchUp and open the SketchUp Preferences. In that side bar there is an Extensions option. Click on that and choose the Install Extension Button. It may ask you if you trust this plug-in. Choose yes.
Step 2: Now We Are Ready to Get Started!
This works best if you are using a JPG or TIFF extension.
Choose File -> Import
Choose your image.
Step 3: Start Creating the 3D File
This is a long and tedious process. Don't give up hope, your almost there!
Step 4: Checking for Holes
One trick I found that helps is drawing a line between the part that is supposed to be filled in. If it doesn't fill both sides you have a hole.
Step 5: 2D to 3D in SketchUp
Use this Push/Pull tool to raise/lower parts of your image.
You can even add a base if you wish by making a square under your drawing.
I made these as a medallion for a few friends that were leaving our HackerSpace.
Step 6: Making a STL File
Choose File -> Export STL
Choose yes when it asks to export the entire module.
Depending on the complexity, we now need to repair the file with NetFabb.
Upload your file to http://cloud.netfabb.com. They will repair the file for you. After a few minutes you should receive an email with a download link to the repaired file.
Step 7: Congratulations!
Send your file to http://www.shapeways.com or to your 3D Printer!