How does one make a character?

Making a character model and all the related assets is usually done using a 3D software package for the modelling and animation, and an image editing package for the textures. Many people who use Unity also use Blender for their 3D modelling because it is powerful and available for free (www.blender.org/). As for texturing you can use whichever image-editor you prefer. If you are looking for a free option, GIMP is likely the most powerful ( www.gimp.org).

As for the actual work of making the model and animating and skinning, there are many resources available, and you will have the best luck finding them if you search for Blender-related tutorials.

Here are a few resources I've found helpful:

General Blender tutorials from the ground up

Full character creation tutorial series (Haven't used it, but it looks good)

Character rigging

Creating a walk-cycle with the Blender Rigify addon

There's a lot to learn when it comes to making a character, but hopefully this provides a decent starting point. There are many more tutorials out there that can help you with your more specific needs.