You can search for pre-existing models on the Internet to print as they are, or to modify using 3D modeling software.
Tinkercad - a browser-based 3D design platform, now part of Autodesk (free version available)
Fusion 360 - free CAD + CAM software for hobby, non-commercial design, and manufacturing projects
List of additional free software packages from 3ders.com
Slicer software prepares files for printing by converting your file into machine-readable code. This software can allow you to estimate the amount of time and material a print will consume.
How do I make a solid model (Rhino)
How to fix and repair your 3D files (Shapeways)
Tips for designing 3D printed parts (Hubs manufacturing services)
3D Printing Price Check - Calculate how much your print would cost at a variety of pay-for-print services