Layers

Layers are like a stack of images which you look down on from above to see the effect, so as you are adding more layers they are generally added to the top of the stack so that they affect all the layers below them.
New Layers are added above the Layer which is highlighted.
Lock Icons. Locks transparent pixels so they can not be painted over, only the image area. Locks the image from being edited. Locks layer position from moving. Prevents auto nesting. Locks all.

Opening an Image

Images open with the original image as a Background Layer.
Background Layers have a limit as to what can be done to them but Double Clicking on the Layer panel gives the option of changing it to a normal layer.

ALT + CLICK on the eye symbol for a layer toggles all the other layers on and off. Useful for a before and after view.
Double Click on a Layer Icon to open its Properties Panel if it is not already open.
Double Click to the right of the layer to bring up the Blend Modes panel.
ALT + CLICK towards the bottom of a layer icon and a small square appears, drag it down to the junction with the next layer below and CLICK and it creates a Clipping Mask so that it only affects the layer below.
SHIFT + +/- - Toggles between different blend modes. Ensure the Move tool is selected. [Also in Layers] [Also in Blending Modes]
CMD + E merges all selected layers into one layer. (or layers in a group??)
CMD + ALT + SHIFT + E Created a merged layer of every visible layer as a single layer above all the other layers with out altering any of the other layers. this is Calle ‘Stamp Visible’. This is not in a menu. Make sure the top layer is selected first so that the stamp appears as the top layer.
CMD + ALT + CLICK on a later selects the contents of that layer, even if it does not occupy the whole layer. Selecting like this is difficult to do otherwise.
SHIFT + CMD + N Creates a new layer above with an option box asking you for the details.
SHIFT + ALT + CMD + N Creates a new blank layer above.
ALT + CMD + G Creates a clipping mask to the layer below.
OPT + CLICK Hides all other Layers except the one you are clicking the Eyeball on. Do this again to turn all the other layers back on.

Layers can be renamed.
Layers can be turned ON and OFF by clicking on the Eye Icon.
Layers can be copied and pasted. Highlight a layer. Press CMD + C. Go to another document and press CMD + V to paste it. (Ref)
Resize layers from the centre with SHIFT + ALT. The anchor point in the centre can be dragged to another point and it will then rotate from this new point with SHIFT + ALT. (Ref)
Individual layers can be rotated when in Transform mode (?) by right clicking and choosing Flip Vertical etc. Also rotate by dragging the corners from outside the bounding box, or hold SHIFT to rotate it at 15 degree intervals. (Ref)

If you have the texture visible in Finder, then drag and drop it into the Photoshop program icon and it will open as a smart object. (Ref)
Open the image in Photoshop. Click CMD + A to select the whole of the image. Click CMD + C to copy the image to the clipboard. In the document you want to open the image in click CMD + V to paste it in as a new layer. (Ref)
Drag the image from the Finder and release it in the editing area where you want it to open. This produces a new layer which is a Smart Object. (Ref)
Layers can be copied and pasted. Highlight a layer. Press CMD + C. Go to another document and press CMD + V to paste it. (Ref)
(Links from Adding Textures to Images)

Groups are like folders, which are useful to tidy up a stack of layers and group similar ones together.
Create a Group by highlighting the layers you want to add and clicking on the Group icon at the bottom of the Layers panel, or using CMD + G, or right clicking on the selected layers and choosing 'Group from Layers' in the menu.
A Group can have a Layer Mask and can also have an Adjustment Layer clipped to it, which can also have a mask.

A Clipping Mask is simply a mask that is clipped to the layer below it, so that it only effects that layer and not everything else under it, as it normally would. This can be really useful for limiting the effect of this layer only to the precisely masked area of the layer below.
A Clipping Mask is indicated as being present in a Layer when there is a small downward pointing arrow next to it.
ALT + CMD + G Creates a clipping mask to the layer below, or use Menu > Layer > Create Clipping Mask, alternatively Right Click on the Layer and select Create Clipping Mask.
OPT + CLICK also create a Clipping Mask by clicking where two layers join and the Pointer icon changes.
Most Adjustment Layers also have an icon at the bottom to create a Clipping Mask.
Be careful not to move or add any other layers immediately below the Clipping Mask as it will automatically clip to the layer below it. It is often better to Group Layers and Clipping Masks together, as otherwise any layers that are moved can clip to these or unclip them.
Clipping Masks can be added to a Group.
Clipping Masks can be stacked one above the other and each of them only effects the actual image below.

Photoshop Layers Window