There are LOTS of bunting tutorials out there, so I'm by no means re-inventing the wheel. Just sharing how I do it if you like it.
Step One: Pick out your adorable fabric and cut it into triangles. Any size you want. Two triangles for each piece because it's double sided. I honestly don't remember what size I made Leeland's-- the baby shower bunting I made has triangle dimensions of 8 inches across the top and 9 inches down both sides. The birthday bunting, since it was going to be long (Happy Birthday takes quite a few triangles), I cut down the width a little, 7 inches across the top and 9 inches down both sides.
*For the "Happy Birthday" I used Heat-N-Bond and cut them out of the black fabric and ironed them on. I reinforced them with a zig zag stitch all the way around. I didn't want my letter stitching to show through on the back side of my bunting, so I sewed the letters on before I sewed the pieces together and then when you flip it right side out you can't see any of it.
Step Three: Iron all the triangles flat. (I've found this step to be pretty important for the overall look and so that you can get your top stitching straight, so don't skip it.)
Step Four: Top stitch the two downward sides of the triangle. I use a zig zag stitch for this because I like the way that it looks in the end. Remember, the top part of the triangle is still completely open, do not sew the top. For the top stitching I match the thread to whatever color bias tape I use to put them together. You could match your thread to your bunting fabric, but when you're using a variety of fabrics, that would get to be a lot of thread changes and quite frankly, I don't have the patience or enough bobbins for that. So if you look above at Leeland's, I top stitched with red, for the birthday one everything is top stitched black.
Step Five: Sew all of it together with bias tape. I use double fold bias tape and it needs to be at least 1/2 inch wide, though it could be wider. Open it up and slide your triangles in. (This is where the top finally gets sewed closed.) I find it easiest to just add in the triangles one at a time as they're going through the machine. (Who needs pins!?) And I use a zig zag stitch for this as well.