The slipstitch is a hand-stitch that starts from the back (interior) and goes through all the layers of fabric except the frontmost (exterior) layer of fabric, before coming back up through all layers to return to the back. Generally, you want to put your finger behind that last layer of fabric and if you feel the needle prick your finger, you pull back just enough to feel that layer of fabric "slip off" before pushing the needle back towards where you put it in. This means that the stitch remains "invisible" to the outside of the garment. It also means you'll learn the value of "light touch" very quickly or you'll need to get in good with your local blood bank (I've always been an elbow-grease kind of girl myself, this is a new horizon for me).
I recommend using a smaller, thinner needle for this -- a larger, thicker needle is going to be harder for the fabric to slip off of, and will make a bigger hole in your finger if you get carried away.
It's always a good idea to practice the slipstitch before you have to perform it for real--this is a tricky stitch to master! All you need to do is create 3+ layers of fabric to join. You can do this by copying the little pocket I created in the video, or simply by folding some fabric in half and then folding it in half again, and then picking which side you want to be the front and which side you want to be the back.