The technique used is called ruching. Use a long thin needle with a small eye and sewing thread (if you find your thread breaks when you pull up the gathers you should try a stronger thread like a beading thread). Use white thread for light ribbons and black thread for darker ribbons, I have also used invisible thread but it is a bit tricky to work with. The amount of ribbon you require will depend on how tightly you pull the ruching and the weight of the ribbon. For yesterday's card I required a length of ribbon about 3x the length of my finished piece. I left my ribbon attached to the roll until I had finished stitching and gathering the ribbon to the desired length and then cut the ribbon for less waste.
Below is a picture showing the zigzag pattern that you hand stitch onto your ribbon. Begin stitching at the top edge, starting with a couple of back stitches, (do not knot the end of the thread and start that way as the knot will most likely not hold and will pull through your ribbon when you start pulling on it for gathering), and make small running stitches diagonally to the other edge of the ribbon. Take your stitch over the edge of the ribbon (I have tried to show this in my hand drawn diagram), make a right angle and continue stitching back to the top edge.
Once you have stitched as much of the ribbon as you think you need, pull on the thread and gently gather the ribbon, pushing it towards the start end. Pull it as loose or as tight as you like depending on how you want the finished piece to look. I leave my threaded needle in the ribbon in case I need to add more stitches. Once you've got the finished length take a few back stitches and cut the thread and ribbon.
I hope that is clear. Leave a comment if you have any questions.