So I knit a row and the knitting is on row A. Then, because I knit with my left, I hold a on my left. Then I knit a row so now the knitting is on B. Then I switch so now I’m holding B on my left. So in other words I’m holding the empty stick on my right? What kind of stitch is that?????.?
If you filled your right needle with stitches, and then swapped hands so that the full needle is now in your left, it’s simply time to start knitting the next row. What stitch you choose to do is up to you. You could use knit stitches, in which case you would wind up with garter fabric, which is reversible and nice for scarves. Or you could do purl stitches, in which case you would wind up with stockinette fabric, which is not reversible and tends to curl. Or you could do a combination of knits and purls or tweak the stitches around into lace or fancy textures.
A lot of people have trouble with the second row because they over think it. I’ll go through it slowly. With your working yarn hanging down, examine the first stitch. It is probably more loose than the other stitches, specifically, the collar around it’s base is probably bigger than the collars around the other stitches. This is normal, but you do need to take it into account. Use your thumb to stroke that collar downward, and hold it in place while you move the yarn UNDER the needle and to the back, and then wind it around the fingers of your left hand, however you are used to doing it. Now use your left thumb to keep that loose collar out of the way while you insert the tip of the right needle into the first stitch, making sure not to hook that loose collar in the process. Either wrap your yarn around the right needle tip, or use the right needle tip to hook the yarn, and pull it through the stitch on the left needle. Let the old stitch from the left needle drop off. Now it should look more normal to you and you can continue knitting.