Hey there. It's hard to tell from your last photo if that is a stockinette stitch or a 1x1 rib stitch. But I think what you're talking about is you want a stockinette stitch. Like this:
When you knit across your row and you have worked the final stitch and now all of the stitches are on your right-hand needle and your left-hand needle is empty all you do is switch hands. Now the needle with the stitches is back in your left hand and your right needle is empty.
To work a stockinette stitch you knit all of the stitches on one row. Switch hands and work the next row entirely in the purl stitch. You do one row knit, one row purl. To easily tell what side you're on just look at your stitches. If the side you're looking at and about to work with has little "v"s then you need to knit all the way across. If it looks like little waves of bumps, you need to purl.