It's an odd way to phrase the rt and lt, but basically for the right twist, you're knitting the second stitch from the end of the needle first, then the stitch closest to the point second. When you slide them both off the needle together, they're twisted like a mini cable. As you do this, the stitch that you knit first will stay in front of the stitch that you knit second.
For the 'in back of' one, you're knitting the second stitch from the end through the back loop, then the first one through the back loop. The stitch that you knit first will automatically go across the back of the next stitch.
Just do them, and it'll work out--all you need to do is either knit in the front loop or the back.
To slip a stitch, you just move it from one needle to the other without wrapping it.
A YO is when you put the yarn to the back if you're purling or to the front if you're knitting. When you do the next stitch, you'll create an extra stitch that creates an eyelet. Amy has video on yo's.
When it says to drop stitches off the needle, you do just that. Let them slide off the tip.