These are the basic tools: pencil, drawing square, utility knife, Exacto knife, long straight edge (I have a three foot steel ruler) and the mat cutter. Of course, I should add a flat table and a hand clamp to hold the straight edge firmly in place. But more about that below.    

If cost is a factor, keep in mind that having a shop custom cut a mat for you will usually cost you more than the materials and supplies we are talking about.

I have used a cutter made by Logan for a good number of years and I am still using it these days. It has replaceable blades, can be adjusted for the depth of cut, and is rugged enough to be thrown in a drawer. You can buy one of these units on the internet for about $25 (include an extra set of 10 blades for about $2 more). You could consider buying their hobby kit that comes with a simple board, straight edge and "utility knife". It will run you about $50 more. But the main item is the 2000 series cutter. I am not promoting Logan, it is just that I have one of their cutters. For more details go to their website (also take a look at the published manual that describes how to use the cutter):  
  http://www.logangraphic.com/products/boardmounted/  

Let me point out right now that this modification was my idea after using a kit for several matting experiences. (Be careful how you spell "matting", Jay.)  It is not for everyone and I would recommend you try a simple kit, gain some feel and confidence in cutting mats and then decide if you want to make the simple additions I developed.
So, let's cut some mats. Oh, I forgot, you have to buy the mat material you are interested in. Sheets 30 x 40 inches are available in art supply stores in a wide variety of colors that include textured or special featured designs. Most have a white interior layer, some have black or even colored edges.
Let's say that your child (or favorite pet) made a nice drawing that you want to save; you even like to have it matted and framed. You pick out some material for a double matted, but small, display. You want the green to be an edging and the white for the front or outside layer.

You happen to have an old frame you think might be OK. But it has an odd dimension of 13 x 10 inches. No problem; let's see what we can do. You make some measurements of the picture, decide how wide an edge you want with the green, and jot this down on a piece of paper. You decide the green mat should be a bit dominant and be 3/8th inch wide. Make a rough sketch. The white edge will be a bit narrow, but otherwise this should be fine. Now you cut two pieces of mat material to 13 x 10 inches (one green, one white).

Make a layout of the picture size, 7 x 10 inches, on the back of the green mat first.
Repeat: The first opening will be on the green mat, the one next to the picture! So you draw the rectangle carefully on the back side, making sure the dimensions are centered. Now you are ready to make your first cut.
Note: always draw the design and make your cuts on or from the back side.

Put a layer of scrap material underneath the cutting area so the blade will not cut into the table surface (you could even used your wife's plastic pad she uses for cutting fabric.) Then place the guide along the pencil mark for the first cut, clamp it firmly to the table. Align the cutter so the scribed line is about 1/16th of inch out from where the cut should start (more about this later). Push down on the cutter making the blade go into the mat and slide it along the guide while you hold the guide firmly in place. Stop when the cutter is about 1/16th beyond the vertical line representing the end of the cut.

Voila, your first cut . . . but don't look! Just lift the guide and rotate the mat counterclockwise one quarter turn. Repeat the alignment and cutting process. Do this two more times and you should be finished!

When you carefully turn the mat over you may notice that a couple corners are not quite cut through. You can finish this with an Exacto knife held at about a 45 degree angle. The reason for this "not-quite-all-the-way" cut may be that the depth of cut is not enough or that the blade was started and/or ended not far enough beyond the line. Experiment and find out what is good for you.

For the opening of the second mat (white in this case), you trace the size by inverting the green mat onto the back of the white. Line up both sheets, hold them in place and use a pencil to outline the four corners. Notice the piece of masking tape near the tip of the pencil. This is done to prevent an ugly smudge on the cut edge of the green mat. Just the tip protrudes as the taped pencil slides along. Be sure to hold the pencil vertically. Slanting it would cause the tracing to be off. This technique is also useful when you want to make several designs with the same pattern and dimensions.

So now we have the corners marked on the back of the white mat. Carefully pencil in the width of the border, 3/8th inch in this example, and draw the four lines where this mat should be cut. See above. Make the cuts and  . . .now you have your first matted artwork!

Just a couple notes in case you want to explore from this point on:

1. Practice making a couple more of the above and really feel like you know what you are doing. The material is relatively cheap and your time is your own. Then experiment.

2. Always draw the pattern on the back of the mat.

3. At the intersections, add right angle lines to show where the corners are. Label them if necessary. What I mean by that is shown in the example below. It shows you where the cut should start and end.

4. Make the cuts so the part to be eliminated is in front or away from you as you line up the guide. That way you will have the beveled edge of your cut mat in the right location. Take a close look at the pieces you have just cut. Would you want the piece you cut out to be part of your matting?  No, it has the bevel on the wrong side.

Let's do another example with some unusual cut-outs. I drew the above on the back side of a piece of blue mat. Notice the extra lines at right angles to where the cuts should start and stop. I normally don't draw the outline this heavy, but this time I wanted the lines to show better for these photos.

Here is the result after I made the cuts as outlined above.

Now it is your turn.                               (To top of the page)