setup:

Once you download the material, you will get a .zip file with a .blend file inside. This contains a small scene with the material applied to a few demo objects. Unzip the file with your tool of choice (for example, 7Zip). Once it is unzipped, there are a few ways to go about getting the material into your blender scene

First method: linking

Open whatever scene you want to use the material in. Go to the "File" menu in Blender, then go down to and select "Link." Locate the .blend you downloaded, and click on it. Blender will show you a list of things you can link. Select "NodeTree", and then "Lego-Shader-X" (where "X" is the version you downloaded). Now, when you go to an object in your scene and edit it's material, you can add the new material as a node group.

This method is preferred, as it allows you to make changes to the node group in the original "Lego-Shader-X" file, and have those changes automatically propagate across every file you linked it to.

Second method: copying

You can also just go into the downloaded .blend file, open the node editor, and copy the node group. Then go into whatever file you want to use the material in, and paste it in there. Alternatively, just copy and paste the enitire demo object into your new scene.