There are some great vidoes at [
www.knittinghelp.com] which you may find useful in viewing how "standard" Western knitting is done. As others have mentioned in response, there can be more than one way to form the knitted stitch and it's the end result that matter.
That being said, knitters can hold the working yarn in either their right or left hands but standard knitting moves the stitches from a left needle on to a right needle.
Looking at the loops on your needle like little legs, in standard Western knitting, the right leg of the loop should be on the side of the needle closest to your body and the left leg of the loop will be on the part of the needle away from your body. The working needle tip will be inserted into the right leg of the loop -- this is often times called the "front" loop. Looking down the shaft of your needle towards your needle tip, in standard Wester knitting the yarn is wrapped counterclockwise around the needle tip. Doing this will ensure that the stitch mount for the next row will keep the right leg of the loop to the body side of the needle.
Some knitters will insert their needle tip into the left leg of the loop which on a standard Western mount will be considered the "back loop" but for some knitters the left leg may actually be on the side of the needle closest to the body.
To determine if you are knitting "correctly" if you create stitches were the base of the loop is open, you are creating standard stitches. If the base of the loop is crossed, which is a technique used to create certain textures, this is not a standard stitch. As long as you know how to create a stitch with an open base and what to do to create a stitch with a crossed base you are knitting correctly. However, if you are knitting in a non-standard way, you will need to understand what you need to do to obtain the final finished look for a given pattern and you will need to keep in mind that technique instructions are generally written with a standard Western stitch mount in mind. In other words, knitters who knit in a non-standard way must be prepared to adjust technique instructions which are written with a "standard" method in mind.