Cutting like a samurai.

Okay, we've picked our pattern, we've got the fabric (maybe a little more than we need ;) and now we're finally ready to cut! Let us start with a basic lesson in fabric and quilting terms related to cutting. The first term that really threw me off was selvage. Selvage? Right....Well, a selvage is a part of every woven fabric and it's the edges where it's attached the loom. On most printed cottons and flannels it is easily identifiable not only because on one side of the fabric is usually white with print on it and on the other it is either white, or the color of fabric, but has noticeable little holes in it. Batiks are trickier. In the picture below, the batik is on the left, and there really isn't much notice of the selvage except a slightly denser weave. The design on a batik also doesn't usually extend onto the selvage.

Another term you will see in full or in abbreviation is "width of fabric" of WOF. To someone who's sewn, this is obvious, but to others, it's not necessarily. WOF is from selvage to selvage, and almost without exclusion, when cutting instructions refer to cutting "strips" they mean, from selvage to selvage. Typically WOF is between 40" and 45" but never count on more than 40" of usable (ie--not selvage) fabric.
Some patterns also refer to "fat quarters" which are often used in scrappy quilts or smaller, lap quilts. A quarter yard is 9" x 4oish"...A fat quarter is a half yard (18") cut in half at the fold--so 18"x20ish"--hence the name fat quarter: same area, different perimeter, geometrically speaking. If you see little folded up bits of fabric laying all over the place in quilt stores, they are likely (always ask if you aren't sure) fat quarters. Obviously a fat quarter will only have one selvage edge on it.
Our last terms will explain why I don't recommend triangles right out of the gates. Fabric has three "directions": the lengthwise grain, which runs parallel to the selvages; the crosswise grain, which runs from selvage to selvage (width-wise would've been hard to say, methinks); and finally the bias which runs at a 45 degree angle to either grain. The lengthwise grain is hardly stretchy at all (you see in clothing patterns an arrow that you're supposed to align with the "grain" which usually means either length or cross), the crosswise grain has a little more, and the bias, whoa nelly, the bias has some serious stretch, which can be handy, but can also be sad when you're trying to sew to triangles together and they stretch and warp and your quilt ends up looking more like a 3D landscape of rolling hills and valleys. In the pictures below I'm applying the same amount of pressure to all three.
The lengthwise grain. No stretch here!
Crosswise grain--a wee bit of stretch.
The bias...streeeeetchy.

Okay, so there's your intro to fabric. Now let's get a-cutting. You will need three tools: a rotary cutter (a circular razor blade on a stick), a self-healing cutting mat, and a ruler of some sort. For your first ruler, I usually recommend a 8.5"x24" or 8.5"x12 or a 6.5"x24". I like the wider 8.5" because I think they're more useful. Individual brands of these things are really a matter of preference and if you stick with quilting, you will probably end up with multiple rulers, cutters, and mats. There are more gadgets than you can shake a stick at these days.

Now, if you prewashed your fabric, you need to iron it to get it back in the general shape that it was before you washed it (ie--selvages aligned, nice crease along the length of the fabric). If you didn't (and I never do) hooray! You're ready to cut. *A quick note on ironing: try to lift and press, not rub around. Rubbing around distorts the fabric.

Many quilters leave fabric just as it rolls off the bolt to cut it (only folded in half once), but I personally believe that the longer the distance you have to go from start of cut to finish of cut, the more likely you are to slip or get crooked, or any number of mishaps. So I fold mine again, taking the fold from the bolt up to the selvage, leaving the fabric about 11" wide.
Obviously I've just got the corner turned back there so you can see what's what. You'll want it nice and straight before you start cutting, but you want to align the selvage edge (if the selvages aren't perfectly aligned, and they never are, just leave them be) to the fold, don't try to align the cut edges. We're going to square them up. So, if you're right handed, lie the ruler on top of the fabric above and slide it over to the right until there's just a little of each layer sticking out on the right side. Then you will use the dots or lines on your ruler and pick one to line up along the bottom fold of your fabric as shown below.
If your cutting mat has a grid on it, do NOT use this to measure or square up. Mats are not very accurate for starters, but they get less so every cut you make. As you cut on the lines, you put them open with your rotary cutter, and pretty soon they aren't even there any more. I'm not too adamant about how people do things in quilting, but do NOT use your mat as anything more than a surface or a guesstimate (if you just want to see if you have a quarter yard or a third, use your mat, not if you're cutting a 2.5" strip). The other reason I encourage using your ruler to measure is that it's more efficient because you don't have to fix the whole piece of fabric any time it shifts. So, if you've done a little quilting and cut with your mat, now's the time to switch.
Once you're all aligned, go ahead and cut off the little piece sticking out. There are many cutters on the market, so find one that you like. I personally only use the straight stick cutters because I cut with both hands (more on that in a minute). Here is the proper way to hold a straight cutter:
You can see that I've opened the blade, my hand is fairly relaxed and the majority of my motion will be in a downward direction. Many quilters have trouble cutting multiple layers because they put too much forward on their rotary cutter. Because it's a circle, if you put downward pressure, it will roll forward. In the real world I would be holding my ruler as pictured below:
But I have to have a hand to take the picture. Spread out your fingers, using the tips, not your palm and press firmly down, not forward or sideways, but down. Once you're comfortable with your hand position, the alignment of your dots along the bottom, cut off the little guys on the right. Always, always, always close your cutter when you're finished. They are extremely sharp and if you forget where you set it and it's open, you can give yourself a nasty cut. Or your pets, or children, or wayward spouses.

Now the reason I cut with both hands is to save time. I'm not ambidextrous, and my left hand is fairly useless for everything outside the quilting world, but you'll be surprised how quickly your weak hand learns new tricks. SO, that being said, I strongly recommend you learn to cut with both hands. The reason is that then I can square up like this:
And never move my fabric to proceed to cutting. If you squared up with your right hand (or if you're left handed, as above), you will now need to carefully flip the fabric so the squared up side is on your left (or on your right if you're a lefty). Each time you move the fabric a). takes time and b). hinders the quest for accuracy.
Okay, so you've got your square edge on the opposite side of your strong hand and your pattern says you need some width of strip. Most patterns are good about saying X strips, subcut into Y rectangles, squares, whatever, but sometimes a pattern just says you need to cut 35--5" squares. If that's the case, assume fabric is 40" wide and figure out how many strips you'd need. (For that example, you'll get 8 out of each, and therefore need 5 strips, leaving you with five extra squares--extra happens, it's okay). So my first cut is to make 6" squares so I'm going to cut a 6" strip. Line up the 6" line of the ruler with the edge of the fabric (be careful here, some rulers have a half-inch on one edge, make sure it's not throwing you off):
Now, this picture is the reason we measure TWICE, cut ONCE. Although, truth be told, I just read the pattern wrong. Anyway, so I cut a 5" strip. I lined up the left edge of the fabric with the 5" line all along and then also lined up the dots along the fold at the bottom, just to make sure everything is still square.
Then you cut along the right side of the ruler, being sure not to slip around. You can continue cutting strips by just taking the cut one out of your way and moving the ruler down the rest of the fabric.
Once I've cut my 5" strip, in order to make 5" squares, I need to subcut the strip. To do this, I turn it 90 degrees, square up the end by cutting the selvages off (I usually leave it folded in half, not in fourths, like it was when I cut the strip) and proceed to cut just like you do with strips. And voila! You have your squares. You can even layer strips on top of each other if you want.

Bear in mind that a lot of quilts use "strip-piecing" techniques where rather than subcut the initial strip, you sew two or more strips together and then subcut them. Cappuccino doesn't use this technique, but I'll take pictures of another project to show you as it is VERY handy and some pattern-writers don't have you do it when you could.

Happy Cutting! Please don't hesitate to comment or email if you have questions.