Version 1: Stitch in the Ditch
Start by cutting a bias strip of fabric 4x the width you want the final binding to be. For instance, I like 1/2" binding on my corsets so I cut 2" strips. My favorite way of doing this is with a rotary cutter, but employ your own favorite way of cutting continuous bias, there are a ton of ways out there. If your bias is not long enough for your edge piece strips together to get one long enough.
Take your bias tape and pin one edge flush with the edge of the fabric you're binding. I know it looks ripply here, I'm not sure why that is, but make it flat and smooth on the face of the fabric.
Sew down the strip. The width of your seam allowance will be the width of your final bias binding (in this case 1/2").
Fold the bias tape over the edge of the fabric to the back. Then fold the seam allowance in to the fabric, leaving a smooth fold on the back of the fabric that is longer than the seam from the other side (this is key. Back must be minutely longer than front for this method to work). Press and pin in place.