See below for the description of a recommended workflow.
Material library is available in Soft8Soft store in the form of themed packs, for example:
Simply unzip the archive with a library pack to any folder on your computer. After inflating the archive you will see one or two folders (if this is Essential Material Pack):
The 2_80 folder contains Eevee-based materials compatible with Blender 2.80. Inside this folder there are blend files (one file per material). The textures used in the materials are located in the material_maps folder. The folder environments contains 3 variants of HDR images that you can use for the environment (each variant comes in 3 resolutions: 1k, 2k and 4k).
The 2_79 folder (only available in Essential Material Pack) contains the legacy library based on Blender Internal GLSL materials (which was the only variant offered before the revision 5 of the library).
In order to use a library material in a project, invoke the File / Append dialog.
Then navigate to the library folder and click once on the blend file with the material you want to add.
Click once on the Material folder...
...select the material and click the Append from Library button.
Once a material is appended, you should be able to assign it to a model. Select a model, go to the Material tab, click on the small button near the material name (or near the New button is there is no material assigned) and select the appended material from the list.
Eevee-based materials require the environment to be set up, otherwise the materials will look dark and non-reflective. The environment is already set up in Verge3D's default cube project which you can use as a basis for your own app. Alternatively, you can configure the environment from scratch as shown in this video tutorial. You can use either of HDR textures in the environments folder of a material pack for this purpose.
Most materials in the library require models to be UV-mapped. Consider unwrapping your models for best results.
Most of the shaders offer sets of inputs by tweaking which you can create a unique material suitable for your needs.
Besides that, there are special inputs for easy connection of baked normal and AO maps.
Some materials may use high-res textures (up to 8k) which may affect the loading speed and performance. Consider re-scaling the images if your application does not require such level of detail.
For the sake of integrity of your application (which is important if you're transferring your project sources to a third party), you can save the textures used by appended materials in the app folder as described below.
Open the Image Editor (or UV Editor) in Blender. Select a texture from the drop-down menu, and check its file path.
If it appears that the texture is referenced from the material library folder, use the menu Image / Save As to re-save it to your application folder.
Search for other material library textures and repeat this operation until all textures are relocated.
You can check the integrity of your application by moving its folder to another location in your file system. Open the blend file and invoke File / External Data / Report Missing Files.
If any of the textures used in the blend file are missing, a yellow splash warning will be shown at the bottom.