I notice the latest build is 2.77, and I only have 2.76. Do I just download the latest version from the blender website, or is there a way to update from within Blender, or what?
Yeah, just download the new version from the blender website. If you're using for example linux and a package manager, then the package manager will update blender automatically* for you, though depending on your distro it may take quite a while from the release date till this update gets pushed through. So it's always best to just grab the latest version from the blender website.