This is a brief primer for PS layers.  This part is familiarizing yourself with the palette, navigating around the layers.  I’ll add more primers for manipulating layers and masking layers next.  Most of this can be found online, but, here are some random tips.  I’m going to use online images to explain.  I’ll also link to various tutorials as I go in case you want to explore it further. 
This first one is from Tutorial 9: (link to tut, if preferred)
Image #1:

In this image(above), from the palette I see that there is some grass and lettering over a black background.  Two green circles are also in the palette, but, not visible at this time because the ‘eye’ is turned off(clicked).
It is a major bonus if you label all layers.  To change the label on a layer, select that layer, click on it and it turns blue, as in above Image #1, labeled “Current Selected Layer”.  Double click on the word, in this case ‘Background’.  Then, type in a term that helps you identify what is on that layer.  With text layers, the letters typed will appear as the name of the layer.  So, in Image #1 above, the word ‘Layers’ is what is typed.  (Image #3, below,  is what that image looks like with all layers ‘turned on’, meaning not turned off with the ‘eye’.)
~Turned on is a layer that is not hidden by turning off the eye.
~Selected is when you click on the layer and it turns blue.  That layer is the active layer.
There are, at least, three(3) ways to work with the layers palette.
   1 – by using the menu across the top of the work space, under “Layer”.
   2 – with the controls within the layers palette box.
   3 – keyboard shortcuts.
         Shift+Cmd ‘N'(Mac); Shift+Ctrl’N'(Win) = New Layer
         Cmd+’J'(Mac); Ctrl+’J'(Win) = Duplicate Layer
The lowest layer is the background.  If you open an already existing document, the bottom layer is usually locked.  See the padlock icon to the right-hand side of the lower level above.  Either duplicate that layer and work from the copy, or, double-click on the padlock and a box will open up, click ‘Okay’ and the padlock disappears.  With the padlock in place, that layer can not be edited.  It is ‘locked’.
Here is a more detailed image of the layers palette.  I like the labeling on this image from Photoshop Cafe.(linked to tutorial)
Image #2:

 

What follows is an explanation of each component, taken almost verbatum from the PSCafe tut.  It was perfect for explanations.

 
Blending mode: Changes the way the layers interact with each other. Experiment with the different modes.  To blend, there must be a layer beneath the layer you want to adjust(blend).  You are blending a layer with another, so, whichever one is on top, that is the layer you apply the blending mode to.
Layer opacity: Adjusts how transparent each layer is. 0 is completely transparent, 100 is completely opaque.

The ‘Lock’ row of features will most likely come later.  For starters, there isn’t that much we do with locking.  But, it has it’s uses and they are important.
Lock all: If the box is checked the layer is totally protected from any editing.
Lock Position: You can make any changes except for moving the image.
Lock Image pixels: You cannot draw on this layer if checked.
Lock transparent: You can paint on this layer but not where it is transparent.This feature is great for painting within an area.  With the layer selected(highlighted in blue) on one of the green circles from Image #1(above), I drew a blue X over the circle with blue.  The blue was only applied to the area that is NOT transparent.
Image #3:

This is what the layers palette will look like for the above Image #3:
Image #4:

 

As with every other feature of PS, there are several ways to work with layers.  Referring to the panel of controls across the bottom of the layers palette, you can click on each of them, or, for some, you can drag an already existing layer down to the icon. 
Delete: Will delete an entire layer. Either Drag the thumbnail to the icon or select the layer and click on the trash can (delete icon).
New Layer: Click to add a new blank layer. Or, click Shift+Cmd+’N'(Mac) or Shift+Ctrl+’N'(Win)  Or, you can go to the Menu across the top, click on ‘Layer’ and select ‘New Layer’.
You can also drag a layer you want to duplicate down to the New Layer icon and it will copy it.  You can also click Cmd+’J’/Ctrl+’J’ with the layer selected that you wish to duplicate.  Or, go to ‘Layer’ in the top menu bar and select ‘Duplicate Layer’.

New Adjustment layer: Allows non-destructive adjustments to a layer. (Can be undone anytime, even after closing document)  This will open just above the layer you have selected.  Thus, it will affect every layer below it.  To have it only apply to the layer directly below, right-click and select ‘Create Clipping Mask’ on the adjustment layer and it will attach itself to that layer directly below it only.
Another way to apply an adjustment is to select the layer you want to adjust and go to ‘Image’>’Adjustments’ in the top menu bar.  The only thing about doing adjustments this way is that it destroys the layer permanently.  Once an adjustment is made, you can ‘go back'(undo) up to a point.  After that, the layer is un-changeable.
Create a new set: Allows you to organize your layers into folders.  Also referred to as ‘Groups’.

Layer mask: Allows you to paint away parts of your layer without damaging your original image.
Layer styles: Special effects for your layers, drop shadows, stroke, outer glow, etc.  Can be accessed by clicking on the icon, or, double-click on the layer you want to make adjustments on and a window will open up.  These effects, though applied directly to the layer, can be turned off and on with their very own ‘eye’.  Here is an image of some layer adjustments, a drop shadow and a stroke around the perimeter of the square (the yellow ‘stroke’ doesn’t show under the yellow overlay I put there).  They are on their own layer, meaning they can be turned off and on, or deleted.:
Image #5
 
Non-destructive refers to making an adjustment over, or to, a layer that leaves the actual layer itself un-affected.  This enables you to be able to go back at any later time and change the adjustments or just turn them off.
Notice that the blue ‘X’ I drew is on top of the upper green circle in Images #3 & #4.  I did that to show the Transparency Lock, but, looking at it now, that layer is ‘destroyed’.  The ‘X’ is there to stay!  You could hit ‘undo’ repeatedly and go back to get rid of it, up to a point, but, then, you would lose everything else you’ve done in between.  This is why we aim for ‘non-destructive’ adjustments.  If you save your rough image in .PSD format, you can go back into that document any time you want and make changes.