It's easiest to print objects from predesigned files. A wide variety of STL files, the 3D-printer equivalent of sewing patterns, are available from a number of 3D model libraries. Many files are open source or freely provided for general printing. There are also a number of sites that offer for-purchase STL files that are usually higher quality and provide hard-to-find models. Creating your own CAD STL files is a more complicated process, especially if you're new to 3D printing. Designing your own models requires software expertise, and depending on what you wish to create, can sometimes require advanced degrees, days of work and specialized software.
If you want a way to create 3D designs online, there are a few strong resources at your disposal. These options produce the files you need to use with a 3D printer. You can create new designs, make changes to existing designs and export the finished products using any of the following choices. These free programs are simplified versions of more feature heavy CAD Software, where most 3D files and designs are created.
TinkerCAD does not require a download to function. You can create 3D objects using the web-based platform and print with 3D printers almost anywhere. Many student classes use this platform because it doesn't require much setup. You can create a profile and start building right away.
Blender is a program that has a more robust interface to create detailed objects. It does have a bit of a learning curve, though. If you aren't already familiar with the 3D design, you may want to check out some online courses before diving into Blender.
Autodesk's 123D App offers a few unique solutions for 3D modeling and design. It provides online and downloadable applications that help with several different tasks, including one that helps translate photos in to 3D objects. This site also offers a full selection of downloadable premade files that are ready for 3D printing.
Another option is Sketchup. This is one of the more popular programs that allows you to create simple 3D designs in minutes.