This way of casting on requires 2 needles. Make a slipknot.
Here is a video in Danish - but I am sure you will be able to find an American video as well.
Place the needle with the slipknot in your left hand and the free needle in your right hand. Now knit the stitch and place the new stitch twisted on the left needle (= 2 sts). Again knit into the new stitch and place it on the left-hand needle with the other 2 stitches (= 3 sts).
Repeat the last step until you have the necessary number of stitches.
This way of casting on is excellent when you need to cast on sts in continuation of a row. It can also be used at the beginning of a row.