I must start first off by saying that the shots in this post are of my Canon 7D and whilst most Canon cameras all have the same layout, Nikons do not. This does not really make a lot of difference as the operation of most DSLR cameras are the same, and whilst the buttons may not be in the same place, they do operate in the same or similar way.

Also another important note is that you can program the buttons on most DSLR to do different functions as you prefer, the diagrams and descriptions although are correct for the functions may not operate the same as your camera as these layouts are the default layouts.

The way this will work is I will cover each side of the camera in turn, Back, Front and Top. I am not going to mention stupid things like where the batteries go, or how to attach a strap but the more necessary things as well as somethings that when I first started I just could not figure out. Also I have changed the names slightly to help you make more sense of things and not be too technical.

Front of DSLR

Front of Canon 7D

The front of most DSLR cameras looks the same with the lens mount being in the middle with a release button to allow you to remove it.
Again I will start at the bottom left of the picture and work clockwise.
Lens Mirror
When you remove your lens and see inside your camera, you see the lens mirror. this is the bit that makes you camera an SLR and allows you to see through the viewfinder.

Remote Sensor

This is the sensor used by the camera when being operated by infrared remote control, it is not the same place that a remote camera cable release would use.
Shutter Button
The button your press to actually take the photo, at default settings pressing half way down will start focus and lock exposure, full press will take the shot.
Red Eye Reduction / Self Timer Indicator
This little light is a dual purpose little fella, when using the self timer it flashes to let you know when the shot it going to be taken.
It also works to reduce red eye in your shots.
Lens Line Up Marks
On all DSLR there is a mark to show you where to connect your lens. On some makes of Canon which take both EF and EFS lenses there are two marks.
Red for EF lenses
White for EF-S lenses
To connect a lens simply line up the make on the side of the lens with the mark on the camera and turn.
Flash Button (only on certain models)
On models with a built in flash there is a button to pop up the flash when you need it. This is normally only needed in manual modes as the flash will pop up automatically when needed in auto modes.
Lens Release
To the left of the lens mount there is a large button, this is to release the lens in order to remove it from the camera. Just press the button and turn the lens to remove´╗┐.
How to attach a lens to a DSLR
In order to attach a lens to your DSLR camera simply do the following
  1. Remove the lens cover and lens cap from your lens.
  2. Line up the white or red mark at the base of your lens with the white or red mark on the lens mount on the camera.
  3. If the marks are lined up correctly the lens will just slip onto the camera, do not try to force it, if it does not just slip on you have not lined it up correctly.
  4. Now turn the lens, normally clockwise, until it clicks. Your lens is now on your camera.
How to remove a lens from a DSLR
To remove a lens from your DSLR simply do the following
  1. With one hand press the Lens release button (normally to the side / left of the lens)
  2. Now with the other hand turn the lens, normally counter clockwise, until it comes of the camera. It does not take any force to remove the lens so if it feel stuck make sure you have pressed the release button. Your lens is now off your camera  
Depth of Field Button
On certain DSLR such as the Canon 7D there is a depth of field preview button, pressing this shows you the best depth of field for your chosen settings.

Final Note
Most of the camera buttons have a dual function and in order to make adjustments you need to use either the rear dial or the top dial depending on what you want to change.