You need to cast on as many stitches one after the other as you need to make the width of the item you are making. All the stitches will be on the same needle. After you have as many stitches as you want you will hold the needle with the stitches on it in your left hand and the empty needle in your right hand. The yarn going to the skein will end up attached to the first stitch at the pointed end of the left hand needle after you cast on.
Once you have the stitches cast on and the needles as I said you are ready to start knitting the first stitch at the end of the left hand needle. Then when you have knit each stitch in the row, exchange the needles from one hand to the other so that the full needle is again in your left hand and the empty needle in your right hand. I think of the piece of knitting that you have completed as coming out toward you from the left hand needle and lying between the two needles. It will, of course not amount to much at first, but that is where the knitting will grow.
I know how to knit both styles and prefer Continental, but I actually think learning the English style is easier. I can teach a 5 year to knit that way, but they don't usually have the coordination to knit Continental. I taught my husband to knit and he could do the knit stitch Continental, but not the purl so I had him switch. But if you crochet, or are left handed Continental may seem to make better sense to you. I taught several grown up beginners that way last winter. They had all crocheted and took to it well. Some teachers teach both methods right from the start and let the student decide which one works for them.