Most 3D printers require you to have an STL (STereoLithography) file to print.  You can design your object in any 3D modeling software, such as Solidworks or any of the free software programs shown below.  You can also use or modify a pre-existing file from a design library. If the 3D modeling software you use does not readily export to STL, you may be able to download a plug-in or extension that will do that for you.  Or you can use another software program for that step.  

Free 3D modeling software

• Blender is a powerful, free and open source 3D animation suite you can use for 3D models.  Enable the 3D Printing Toolbox. 
• OpenSCAD is free software for creating solid 3D CAD models - it  might be the application you are looking for when you are planning to create 3D models of machine parts.
• Sketchup comes in free or pro versions. Get the Sketchup STL from the Extension Warehouse. 
• Tinkercad a browser-based 3D design platform, now part of Autodesk (free version available). 
• List of additional free software packages from 3ders.com