Card Making Embossing is quite simply the technique of creating a raised or 3D image on your handmade card.
The effect can be achieved in one of 2 ways - either by Dry, or Blind Embossing as it is sometimes known, or by Heat Embossing.

Heat Embossing creates an effect similar to that on many store bought cards and is very popular for embossing sentiments. Both ways are easy to do but Heat Embossing requires a little more effort on  your part.
For Heat Embossing you will need  embossing powder, an embossing ink pad and a  heat gun.There are 2 ways of doing Heat Embossing:
The first way is to rubber stamp an image or sentiment with a slower drying pigment ink and then before the ink dries sprinkle some embossing powder all over it. Gently blow any excess back into the container and the use the heat gun to melt the embossing powder. The powder starts to turn in seconds and you should be careful not to overheat it as it will cause your image to become blurred. Just gently move the heat gun over the area slowly rather than concentrating the heat all in one spot.
Buying a heat gun may seem an unnecessary expense when you think a hand hair dryer could work just as effectively, however this is not the case. A hair dryer's heat is not intense enough to melt the embossing powder properly - you will get poor results and ruin your work.
The second way is to rubber stamp the image using an embossing ink pad, such as Versamark (this creates a clear sticky image) and then sprinkle the embossing powder over this and then continue as above.
Wiping a small anti static bag over your card before you start to work will stop particles of embossing powder clinging to where it you do not want it to go. If some specks do go elsewhere just use a child's paintbrush to gently brush them away.
If you want to emboss either a freehand drawing or writing then you can use an embossing pen to do the outline and then continue as normal with embossing powder.
Heat embossing is something some card makers seem to shy away from but it really is an easy technique to master and it can produce some lovely results on your cards.
Embossing powders are available in many thickness and finishes - as in all thins card making it is good to experiment to see which best suits you and the work you are doing.

Dry Embossing is something which has evolved over recent years. The traditional way is to work with embossing stencils, which are normally made from brass, and an embossing tool.
You do need a light source to emboss correctly but can emboss holding your work against a window so the daylight acts as your light source.  Place your paper, card or vellum over the stencil and then trace around the edges with the embossing tool. Always work with the wrong side of the piece facing you and this will create a raised design on the right side of the card. This is the sort of design work that you often find on wedding invitations, or high end restaurant menus.
Embossing tools are like pens but instead of a nib they have a rounded ball on the end. They come in different sizes and can be bought individually or in sets. Which size you use will depend on personal preference, the stencil you are working with and the medium you are working on, for example if you are working on vellum then a large ball end will work best.
Most people like to work with a Lightbox. These are relatively cheap and are easy to use. You simply place your stencil directly onto the Lightbox and fix it with a little masking tape or other positionable tape, then position your work accordingly on top of the stencil. The light shining from below the box  will enable you to see the stencil clearly through your paper/card and then you run your embossing tool around the groves of the stencil.  If you allow the card to warm up on the Lightbox before starting to stencil you will get a crisper image.
Leaving your embossing plain works very well but in some cases adding a little colour by gently chalking over the raised parts will also look effective.
Some companies now produce themed embossing boards - these not only help you create embossed areas on your cards but can also help you to create a shaped card or box for your work.
Card makers often spend a lot of time and care producing a beautiful card and then just put it in a plain envelope - by dry embossing a flourish or a flower, or some other suitable image on the envelope flap it can add to the overall look of the work.
In recent years embossing machines such as the Cuttlebug, Sizzix and the Spellbinders Wizard have come onto the market and these have helped raise embossing to another level. they work really well- you place your card or paper which you want to emboss inside a plastic wallet which has a design on it, and then depending on the brand put that between some pressure plates and then simply run it all through the machine.
Although the actual machine is quite an investment there are numerous different design embossing folders available and they are relatively cheap to buy. Cuttlebug even do a version of their machine aimed at getting children interested in crafting, called "CuttleKids".
The beauty of these machines is that as well as using them for embossing you can also use them for die cutting and a lot of the dies are interchangeable between machines - for example Spellbinders Nestabilities work well with the Cuttlebug as long as you follow the instructions and put the pressure plates in the correct order.