Basically layers control the visibility of things in SU. If you have geometry on one layer which you then turn off that geometry will be hidden. Its important to remember that visibility is all the layers control, they dont work like photoshop where things on layers are separated.
The basic workflow with scenes is to draw everything on layer0, then when youve drawn some things, turn them in to groups and move them to their respective layers. Its very important that you draw everything on layer0 to start with, as otherwise youll get geometry all over your model, and its a real beast to sort out.
Just to give you an example, say i was doing a quick interior. Id first draw all the walls, doors and windows, group them and then put them on a layer called 'walls.' Id then start adding 1 arrangement of furniture, id put all this on a layer called 'furniture 1'. Lastly id do another furniture arrangement, and put all that on to a layer called 'furniture 2.' This would allow me to show the model to the client and switch between the 2 arrangements of furniture simply y toggling which layers are on and off.
To answer your second question, you dont need to use scenes with layers, although you can. As default i think SU is setup to save the visibility of scenes when you add a new scene, so if you ad a new scene when youve got a few layers hidden, those layers will be hidden each time you go back to that scene. This can provide a quick way of switching between views, which is pretty cool.
If we go back to our previous example, you could save a scene with 'furntiure1' visible and then another scene with 'furniture2' visible, then youd be able to quickly switch between the 2 layouts with minimal messing about in between.
Lastly, the organiser is a different thing entirely. Its is basically just a folder tree sort of arrangement to display what groups and components you have in the model. If you want to use it it is very important you name all your groups and components, as otherwise it just become a large incomprehensible mess. It would be quite OT to go in to any more detail here, so i'll just link to the rather useful google vid here: Very un-usefully the vid has disappeared grumble, all i can suggest is to have a play around with it, its fairly self explanatory.
p.s. this might be more appropriate in the newbie forum.