I am new to knitting and have been practicing the Continental style.
I don’t know why my knit and purl stitches appear to be twisted. What am I doing wrong?
If you hold the yarn in your left hand but wrap the yarn around the purl stitches the opposite way from standard (perfectly okay if that is what you want to do, and compensate or it) it will cause the stitches to be twisted on the next row if you knit them through the left side of the stitch loop in front of the needle. I choose to wrap my purls the other way so they don’t get twisted, then I can knit them as I said. If you want to purl the other way you need to knit your stitches behind the left needle going into the stitch loop right to left to untwist them. But… I think doing this only twists every other row. If all you rows are twisted I’m not sure what you are doing.
If you want to twist and then untwist so they end up not being twisted 
check out something called Combined knitting. If you don’t want to twist at all watch Amy’s video on this site about how to purl in Continental.
I was going to suggest you look at the videos, too.
Here is some more help. Sometimes it helps to look at other videos/pictures as well.
http://www.knitpicks.com/tutorials/Knit_Stitch_Continental__D9.html
http://www.knitpicks.com/tutorials/Purl_Stitch_Continental__D10.html
It sounds like you’re not always wrapping the yarn around the needle the same way each time. I suggest you knit slowly and consciously practice wrapping the yarn around the needle until it becomes a habit. In continental and English knitting, you will wrap the yarn over the needle and away from you. I suspect you may be wrapping the yarn over the needle towards you some of the time. That’s the wrong direction. Think of some kind of memory hooks that will be easy to remember. You’re a big bad monster and the yarn is running away from you. Your yarn is running over the hill (needle) and down the hill away from you. This is the proper direction. You will do this for both the knit and purl stitches.
Edit: If you’re not putting the yarn over the needle the same way each time, your stitch orientation will be wrong. This will result in twisted stitches. This video will explain to you about stitch orientation. It shows how to knit Eastern European style. Just so you don’t get confused, you can skip the second part of the video on how to knit in this style. In the first part of the video, the poster explains about stitch orientation for both the Continental/English and the Eastern European orientation. The Eastern European style does it the opposite way. Ignore that. She shows how to wrap the yarn over the needle. You can replay this video as many times as you need to.