Matte board
From Silvergrain Labs
Windowed matte board is usually used to mount photographs. Matte board comes in 4-ply, 6-ply and 8-ply thickness. 8-ply matte board is heavy, pretty expensive, and very difficult to cut nicely, but it's worth the trouble to use 8-ply matte for large prints, such as 20x24 prints.
My standard supply is 3/16" acid free foam core board for backing board, and Alpharag Artcare 8-ply matte, 8660.8634.8 white.
8-ply matte is hard to cut straight, and beveled edge window cut is even harder. A professional quality matte cutter (upward of $600, such as Logan Framer's Edge) is much easier to use but they take much space and money. With some practice, it is possible to cut and window 8-ply matte with hand tools.
A combination of a heavy stainless or aluminium ruler with antislip pad and an Olfa MC452B matte cutter (45 degree beveled edge, about $30) is inexpensive and easy to use, but with 8-ply matte, the challenge is still pretty high. I've tried similar hand cutter made by Logan (also $30 range). The Logan hand cutter is made of aluminium and looks well made, and indeed it works well with 4-ply and 6-ply matte, but it doesn't penetrate deeply enough to cut 8-ply matte. Olfa cutter is made of transparent plastic, and looks cheap, but it's rugged enough and it's good because you can see the lines you draw on the board through it.
Never try to cut a matte board when hungry. Have a lunch or snack before working.
Straight cuts
Matte board should be cut to the size of the frame. It may require several cuts to cut through the matte, as expected. Use a fresh, thin-blade sharp knife (like small xacto knife, or Olfa snap blade knife) for the first shallow cut, and then use a thicker, stronger knife for the next few cuts, and back to a thin knife again for final cuts. The idea is to cut the surface with a thin, sharp knife, which is much easier to keep the edge clean. (Thick knife is good for deepening cuts, but they are terrible in making clean first cut.)
Replace knife blade frequently. The cost of blades is pennys. The matte is a lot more expensive. The labor for redoing is even more expensive.
Window cut
On the back side of the matte board, draw lines to cut the window. It's best to use mechanical pencil to draw sharp line, so that there is no ambiguity while cutting. Then follow the instruction for MC452B to cut the matte. It's important to use firm cardboard under the matte board, because self-healing cutting board is not very good for cutting windows. (The soft plastic board grabs the blade and makes it harder to make final cut. It also has higher risk of chipping the blade tip.)
I found that it is very important to make a good straight first cut that is sufficiently deep. To do this, the blade tip has to be absolutely sharp, but this is where it gets dull rather quickly. Don't be cheap here! Replace blades frequently.
Replacement blades for MC452B is MCB-1, about $10 for pack of 5, which isn't very cheap. Each blade is good for a couple of 20x24 windows on 8-ply. (Blades last much longer with 4-ply.) If you cut a lot of 8-ply matte, you should have Logan Framer's Edge matte cutter or something of that caliber.
Replace knife blade frequently. The cost of blades is pennys. The matte is a lot more expensive. The labor for redoing is even more expensive.
If there's any loose pencil lead dust or stain, clean it up with kneaded plastic eraser (used for pencil drawing).