Why should you want to mat & mount your artwork?  Well, the 2 basic reasons are for protection, and to enhance it.  It's really pretty simple...

In the dim, dark past of art shows, most people would generally hang their artwork in shows.  JUST their artwork.  Generally this was simply a bulldog clip grabbing the top of the paper the art was drawn on.  This would allow the paper to curl, to slip out of the clip, to tear, to be generally man-handled...

And really, just how appealing is a (generally) white piece of paper against a (generally) medium-brown peg-board backing?  Especially if it's curling...

Matting your artwork is really very easy to do.  You can use pre-cut mats, or you can cut your own rather simply.  If you use pre-cut mats, there's less work, but your are limited to the sizes you can find at your local store, as well as the colour selection they have.  Cutting your own give you the most flexibility, but requires an initial investment (which does not need to be that great.  You can start out with basic equipment for $30, or go as high as a wall-mounted system for over $1000.)  If you are going to cut a lot of mats, you want to spend a little more, and get quality equipment.  If you use it a lot, the cost per mat will be much lower than buying them individually (and you'll get a higher quality product).

The first thing you have to consider when using ANY kind of mat is "is it archival?"  That is, is it acid-free?  Paper that is high in acid will start to turn colours over time, spoiling the image you've worked hard to make.  In turn, if the matting material you use is high in acid, the acid will be transferred to your art, and the same thing will happen.  Always look for acid-free materials, in the paper you use to draw on, the matting material you'll mount it on, the material you use to mount it to the mat, as well as the backing material you use.  If one is not acid-free, then it will contaminate the others.

Any good art-supply store will carry acid-free matting material.  You can also find either acid-free cardboard, or acid-free foamcore as a backing material (to make the completed product sturdy).  For mounting it, you want to use acid-free mounting materials as well.  These could be mounting corners that you put the artwork into, or acid-free tape.

NEVER use Scotch tape, masking tape, or package sealing tape.  Scotch 811 (low tack - blue core) or drafting tape are not good, but are marginally acceptable - if it's ONLY temporary (but I'd never use them).  And NEVER use duct tape or fabric tape (I've seen it happen.  It will leave a sticky residue that you can never remove, which will be highly acidic.  Where that tape was will be a stain within a few years - I guarantee it.)  When in doubt, you can check the acid content of any material with an PH testing pen (available at an art store, or a printer's supply store).

You have all your materials - now what?  Well, in the case of a pre-cut mat, just center the artwork as you like it in the opening, and either secure the mounting corners, or use a couple of small strips of tape at the top.  Do NOT tape it on all sides - you want the picture to be able to move just a bit.  Otherwise, if it is placed in an area that has a different temperature or humidity than where you sealed it in, it will "buckle", and that won't look very good.  As long as it's securely mounted so that it won't fall out, that's all you want.

If it's not a pre-cut mat?  Well, then you need to determine the outer size of the mat you want to use (and try to use a "standard" size, such as 9" X 12", or 11" x 14", or the like - making it 8.75" x 15.666" will drive whoever buys it crazy when they try to put it in a frame), and using a straight-cutter (or a sharp utility knife), just cut a piece of mat down to size (remember to cut an equivalent piece of backing material.)  If you have gotten a large piece of mat to cut the section out of, keep an eye on how much is left - you can make one standard (32" x 40") piece of mat got a long way if you cut it "efficiently".

Then, determine the "window", or inner size of the mat.  Just measure the picture area on your artwork, as well as any border area you want, and transfer that centered onto the back of your mat.  Then, measure it again, and make sure that's what you've actually marked on the back.  Then, take your beveling tool (a mat cutter makes a 45 degree cut outward - that's why you cut the back), and working with a straight-edge (or however your equipment is configured) make an even cut from top to bottom on the line you've drawn, making sure to start & stop at the right points.  Rotate 90 degrees, and do it again.  Continue until you're done.  Be sure to use a sharp blade, and a firm, steady pressure.  Always cut just a little beyond the official start & stop points, so that the excess mat material will come away cleanly.  Now you just mount it as above.

You've got the picture on the mat, and now you want to apply it to the backing material.  One thing to check here.  If you are using pre-cut mats, check the backing.  The mat itself is usually acid-free - the backing is generally chip-board - NOT acid free.  If it's the sort of grey, uneven, speckled material most are sold with, toss it and get something acid-free.

If it's headed directly for a frame, or it will be tightly shrink-wrapped, you don't need to secure it to the matting.  Otherwise, use a SMALL amount of double-stick tape at the corners to prevent the front from separating from the back.  Frame shops generally use an adhesive tape gun (ATG), which is really nothing more than a fancy double-stick tape dispenser.  Don't go overboard, use just enough to get the job done - you might have to open it back up again.

Now it's securely mounted.  But what if something touches the artwork (a serious problem when using oil or pastels...)  Then encase it in something.  You can either use a shrink-wrap machine (which many larger shops have), or use tape-on shrink-wrap material (which you tape tightly to the back, then tighten it with a hair dryer), or you can cover it with Mylar sheeting.  This way, your picture is safe in transit, or at a show.

Mats come in so many colours - which one should I use?  Well, if in doubt, you can always go with black.  Basic black works with most everything (except of course extremely dark pictures - use white for that...)  But if you have a choice, try to use a colour in your artwork to "set" the mood of the mat.  Try to use a colour that a central point of your picture uses (such as the eyes, or something similar).  You want to draw the viewer into the picture, and if the mat is the same colour as something you want them to see, their eyes will be drawn to that item.  If you have a lot of one colour, you don't want that as a mat colour (it will wash out everything.)  Use your judgement - what looks right?  Or the reverse - what looks wrong - and you've now got fewer choices to make.

Once you've mastered doing your own mats, you can go on to trying fancy stuff, like circles, or ovals, or cutting designs in the mat itself.  But you'll find that a good mat not only protects the artwork inside, it makes it look much better than it would just thumbtacked to the wall.