Blender's shaders can be found in the Properties Editor, Material tab, Material drop down menu:
It's easy to navigate them because you can start typing the name of the material just after clicking it to search. If you wish to keep the material without assigning it to anything you will need to press the F icon next to the material's name to assign a fake user for it not to get removed when you reload the scene. It's a shield icon in Blender 2.80:
That's about it. You might also find it useful to know the shortcut for linking materials to multiple objects when working with materials. If you have multiple objects selected and assign materials to the last one(active), you can hit Shift+L followed by m to link materials to all the selected objects.
Coming from another software package this is often a huge shock, however once/if you get used to this way of thinking about materials in the scene you might find it surprisingly convenient and easy to use.
There are some useful functions in the Outliner, Blender File mode as well. You can select objects linked to specific material there as well as delete materials and do some other useful things: