One of the big issues that I struggled with for a while was cutting straight strips of fabric from yardage. I always struggled with the bulk of the fabric and would end up with 44" long Z shaped strips. What a waste of fabric.
Eventually (and many yards later) I've perfected a technique that works for me and I've set it out below (along with some very basic pictures).
1. Get your tools ready. You're going to need a ruler that's at least 12" long and at least 4" wide (the wider the better). Your also going to need a clean cutting mat (no pins or lint please - running over a pin with your rotary cutter is a bad idea as I've discovered) and a rotary cutter with a sharp blade. If you can't remember when you changed the blade last you probably need to. And yes, that's a Fons and Porter Klutz Glove in the picture which is now wear when cutting. My New Years present to myself was cutting off the end of my left thumb. Ouch.
2. Check your pattern and work out how much yardage you need to cut right now. Not total, but just for now. Trying to cut 1.5" strips from a piece of fabric 4 yards long is a nightmare - you'll have yards of bulky fabric to deal with and if your workspace is anything like mine, it'll probably end up hanging off the end of your cutting table. This weight will drag your fabric down, causing you to miscut. If possible, try to sub cut your yardage into more manageable pieces, for instance yard wide pieces. If you're just cutting 20 4" squares now, you don't need more than a fat quarter.
3. Tear your fabric into smaller pieces. This is terrifying the first time you do it but it's worth it to avoid dealing with all that bulk. Make a small snip in the selvedge along the cross grain line (ie cutting into the fabric perpendicular to the selvedge) and firmly grip the fabric either side of the tear.
4. Iron. I hate ironing. Seriously, I buy no-iron clothes for a reason. But when it comes to yardage, I always iron. If you buy your yardage from a bolt, the folds are randomly put in by the machine operator at the factory and there is no guarantee that he (or she) evenly fed the fabric onto the bolt. If your fabric was posted to you, the shop will have folded the fabric so it fits neatly into their packaging. To ensure you get a clean cut you're going to need to remove those misleading folds or the fabric will always want to lay in that position again. If you're going to starch your fabric, now is the time to do that too. I iron rather than press at this point as there is no bias to worry about and, let's be honest, pressing yards of fabric takes too long.
5. Fold your fabric once. For me, this is the most important part of this whole process to get right. I have a small cutting mat so I fold my yardage twice so that it fits on my mat. Firstly, pick the fabric up along one selvedge, holding a corner in each hand between your index and middle finger. Hold the fabric taut between your two hands.
Line the two selvedge edges up using your fingers so that they are even and parallel. If you only have none or only one selvedge (because you have a half yard or fat quarter) line up the top and bottom of the fabric. Does the fabric hang straight down from your hands or is there a twist, crease or bubble in it?
If it hangs straights, great! Lay it down on your cutting mat exactly as you are holding it. If the fabric doesn't hang straight, the grain lines aren't parallel and it's not a happy bunny. If you cut your fabric like this, you would end up with wonky pieces.
To line up the grain lines, slide the front piece of fabric a little to to the right, ensuring that the selvedges (or top and bottom of the fabric) stay perfectly parallel.
6. Fold your fabric again. This step is optional but if you've got a small cutting mat like me, you can't fit 22" of fabric onto your mat safely (I've tried, there was blood...). Being careful not to change the way the fabric lays, bring the bottom fold up so that it lays parallel to the selvdge but ends just under the selvdge. This will save you some fabric when you cut off the selvdges. The selvedges and the single fold should now be at the top of your mat, the double fold at the bottom closest to you.
7. Check you are still square. Gently run your finger down the double fold closest to you. If your fabric is square, the double fold should feel the same the whole way across the fabric and you shouldn't feel any gaps or edges in the fold. If you do, you need to repeat the above.
8. Even up the edge. I'm right handed and have never mastered the art of cutting left handed so I trim up the right hand side of my fabric first. I use my whole ruler to line up along the bottom of the fabric to my left to ensure everything is square.
9. I now cut the strips I need from the left hand side of the fabric. Every 3 pieces or so, I check to ensure that the cut strips are straight and, if necessary, I retrim the edge to square it up again.