How do I alter my jeans to have a stripe of contrasting fabric down the outside seam?

Adding a contrasting stripe to the outside seam of your jeans is actually fairly simple.  You just need to remember that for as much fabric as you add in, you need to remove that much fabric from the jeans.

For this project, you will need a pair of jeans, some contrasting fabric, matching thread, a tape measure, a yard stick, pattern paper, a pin or pencil, fabric scissors, straight pins, and a sewing machine.

1. Purchase the contrasting fabric.  Because denim is a tough fabric, choose one that will stand up to the stresses of wearing, especially if the jeans are tight.  Look for colored denim, corduroy or a similarly heavy fabric.  If you use a fabric that is too light in weight, the stitches will likely tear out with use.  Purchase thread to match your jeans.
2. Make sure the jeans and the contrasting fabric have both been washed at least once to take care of any shrinkage.  If you sew them without pre-shrinking, they could shrink at different rates, causing puckering at the seams.
3. Using a seam ripper, open the seam on the outside of the jean leg as far up as you want the contrasting fabric to run.  You'll need to remove the hem on the leg as well.
4. Measure the length of the seam from bottom to where you stopped ripping the seam.  You'll want your contrasting fabric to be cut at that length plus 5/8 inches for seam allowance at the top.  Cut the width to the width you want the stripe to be plus 1 1/4 inches for the seam allowance on each side.
5. Now you need to make your pattern.  Get some light weight paper, and draw the rectangle of the measurements you wanted.  You can get fabric paper at the fabric store.  You will actually be tapering the contrast to a point as you sew, but you can cut out the fabric as a rectangle.  After cutting out your rectangle, measure across the width a few inches from the bottom of the pattern, and mark the center point.  Do this again at a few inches from the bottom of the pattern.  Using your yard stick, draw a straight line connecting the two points.
6. Lay out your contrasting material.  If it is wrinkled from washing and drying, iron it first.  Double the fabric over lengthwise so you can cut out the strip for both legs at the same time if you want to add the stripe to both legs.  Lay your pattern on the fabric.  You want to make sure that you are not cutting on the bias (diagonally, that is), or your fabric will stretch wrong and not lie properly.  Using your tape measure, measure from the edge of the fabric to approximately the center of the line you previously drew on your pattern.  Pin the pattern there to the fabric.  Now move above and below the line a few inches at a time, making sure the line is always the same distance from the edge of the fabric.  Pin again at the bottom and top of the line.  Once you know the pattern is lined up properly, pin around the edges of the pattern so it lies flat while cutting.  You can now cut out the fabric along the edges of the pattern.
7. Once you have your contrasting stripe, lay your jeans wrong side out on the table with the ripped seam up and lying straight.  Lay your fabric strip over the top of the seam face down.
8. Start from the bottom and pin the fabric to the jeans until a couple of inches from the top.  At this point, you want to start tapering the sides up to a point at the top of the blue jeans seam.  You can use a pen or a chalk pencil from the fabric store to draw in the gradual taper.  Pin the fabric along the taper and at the point.
9. Turn your jeans right side out.  You should be able to life up the flaps of the jean material that you pinned over and see the contrast fabric strip.  Using your scissors, trim the jean material to 5/8 of an inch from the seam line with the contrasting strip.  Look at your taper at the top.  If it seems to pucker too much, ease the material and repin to that it doesn't pucker.
10. Now you can start sewing.  Turn the jeans inside out again. Start on one side of the contrasting strip. Sew up the seam and gently turn along your taper at the top.  When you get to the top, sew backward for about 1/2 inch and back to the top to strengthen the seam. Lift your presser foot, and turn the jeans around carefully.  Lower the presser foot back down and sew back down the other side of the leg about 1/2 inch, back up to the beginning, and then all the way to the bottom.  Cut your thread.
11. Using an iron, press the seams open.
12. Go back to the top of the seam to the point you created earlier.  You want to sew a horizontal line across the top of the point, going back and forth several times about 1/2 inch in either side of the point to stregthen the point and prevent tearing along the seam line.  This is why you chose the thread color to match your jeans, so the stregthening line doesn't stand out.  Trim the excess fabric leaving a seam allowance to 1/4 inch around the point so it lies flat.
13. Hem you jeans, and you are finished!