You're doing it right - when you knit into the st below the one on the needle, the one that's on the needle will fall down to the st below it. On the next row, the stitch that you knit below on the previous row will just be a knit, and the one that you knit before will be the one that you knit below in. It takes several rows for it to look like anything but a mess. You also need a multiple of 3 plus 1, the 19 sts will work out.
Look at the pictures in this Fisherman's rib tutorial
(same st, different name) and maybe that will help.