Ok first things first, Over the next few tutorials im going to give a basic explanation of all of the major parts of Maya and how they are accessed. This tutorial will cover the main basic windows you will need to know in order to start using maya effectively.
Firstly everything can be accessed by holding down the space bar, it brings up a universal menu which you can navigate to all other menus.
Hitting Ctrl+A will open the Attribute editor which is where all the magic happens, you can edit polygons, alter materials and even funk it up with fluids and paint effects.
The outliner is a nifty little window which simply shows all the objects and groups in the scene for easy selection
HYPERGRAPH - Rendering
The hypergraph is a graphical representation of the objects within the scene and how they are all linked. It's similar to the shader networks in the hypershade
HYPERSHADE - Rendering
Much like the max material editor this window shows all the materials available to the artist in the scene, they can be edited in the attribute editor. This window also houses the visual representation of your shader networks which allow you to link any attribute of one object/material to another.
GRAPH EDITOR - Animation
The graph editor is a curve based graphical representation of the selected objects, you can view all attributes or just a select few to fine tune those animations
DOPE SHEET - Animation
Another graphical animation window for easy access to keyframes on those large animations. Rather than scaling the timeline you can zoom and pan in the dope sheet.
Thats it for now guys, i know it's really basic stuff but i'll get to the nitty gritty of it all shortly, enjoy!