Bias tape is, simply put, a thin tape made out of fabric that has been cut on a bias (45° from the selvage). It is then folded and pressed in a gatefold with the "wrong side in." You can make this yourself if you have enough extra fabric from your project (post on its way), or you can purchase bias tape from the notions section of your local fabric store (Note, there are many different varieties of bias tape: for most beginning garment projects, you want ½" wide single fold bias tape -- check your notions on the pattern). Try to get bias tape that matches your fabric's design or color as closely as possible.
You're going to see "stock instructions" every time your finish an edge with single-fold bias tape because it follows the same basic 3 steps, so here's what they mean:
Purchased bias tape is usually double-sided, meaning that the interior of the bias tape is indistinguishable from the exterior. The instructions will refer to the RIGHT and WRONG sides of the bias tape, however. The side that is on the inside of the fold is always the WRONG side of the bias tape, whereas the outside of the fold is always the RIGHT side.
The first instruction is to usually open up one of the sides of the tape. Even though it's named "single fold" bias tape, bias tape does in fact have two folds on it. It doesn't matter which side you unfold, but this side becomes the "crease" (the crease of the opened fold), while the remaining folded in side becomes the "fold."
Obviously, the tape is going to be a long, rather unruly strip to work with. So don't worry about unfolding the entirety, just get a couple of inches open and then continue to unfold ahead as you work. Similarly, you might be tempted to pre-measure the amount of tape you'll need and then cut so you don't have the whole spool to wrangle with -- I would highly recommend against this as, if you mis-measure, you will end up wasting a good deal of tape. Just be patient and don't try to do it all at once.
Pin-baste the tape into place along the crease. If the bias tape folds in after you've pinned, that's ok, just flatten it back out as you stitch later on. Work your way around, carefully checking with your seam gauge to make sure that the crease stays ⅜" from the raw edge, until you return to where you started. At this point, you want to overlap the existing bias tape by about an inch, and then cut it. Now, with the overlap, you want to fold the the top piece under (it still want to overlap the flat piece) and then pin it into place.
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Next, you want to trim the seam and clip any curves. I recommend shaving off the ⅛" allowance between the end of the edge of the bias tape and the raw edge. If you want to trim off the bias tape, I wouldn't recommend trimming off more than ⅛" of that, just to prevent yourself from nicking your seam. For clipping the curve, you want to create a notch or two in the curved parts to help prevent bunching when you fold the tape over. Remember: Don't break your stitch!
When you stitch, you'll want to stitch through the remaining fold so that it doesn't unfold and peek out. Remember, the bias tape is ½" wide, and the fold is about ¼" on the inside, so if you stitch ⅜" from the raw edge, you should neatly lock up the fold without slipping off of one side or the other. I generally do this as a top-stitch from the outside, but if you're still getting comfortable with precision-stitching, you might want to do it from the underside so you can keep better track of your allowance. Sometimes, the instructions will tell you to baste before you do the topstitch, I'm not overly-fond of topstitching over a baste-stitch (it creates ratty stray threads that are a pain to clean up), so I just use a pin-baste for this. If you aren't comfortable with pin-basting, do a hand-baste at the absolute edge of the inside of the bias tape, and then machine-stitch just inside the hand baste, then remove the hand-baste.