There are many kinds of 3D design software out there, and different ways to design: computer assisted design (CAD), freeform, or sculpting. Different projects may require different software. Below are some choices you may want to explore.
Tinkercad is free, subscription-based, online software. It's great CAD software for beginners and includes interactive tutorials.
OpenSCAD is free software you can download and use to design solid 3D CAD objects.
On SketchUp you draw 2D shapes and use the push/pull tool to convert shapes into 3D objects. Downloading .stl files requires the SketchUp STL extension. Free and paid versions.
Blender offers freeform "modeling, rigging, animation, simulation, rendering, compositing and motion tracking, even video editing and game creation." Free.
Autodesk has a range of 3D design software for engineering, architecture, product design, media and entertainment. Free trial and paid subscription.
Slicer software prepares your 3D image for printing and interprets your file for the 3D printer.
Cura is Ultimaker's free slicer software and is fairly easy to use. It can be used with other 3D printer manufacturers too.