To slip, take off, or pass a stitch, is to change it from one needle to another without knitting it.
To take under, means to pass the right hand needle through the stitch on the left hand one, so as still to keep the same side of the stitch towards you.
Welts are the rounds of ribbed stitches done at the top of stockings, to prevent their rolling up.
Cast off means to end your work in the following manner: knit 2 stitches, pass the first over the second, and continue the same until you have but one left, which is finished by passing your cotton through it.
To decrease is to lessen the number of stitches by knitting 2 taken together.
To increase, or make a double stitch, is to knit one stitch in the usual way, then, without slipping out the left hand needle, to pass the thread forward and knit a second stitch, putting the needle under the stitch. The thread must be put back when the stitch is finished.
Hang on, means cast on.
Bring the thread forward, means to pass it between the needles towards you.
Cast over is a term I believe sometimes used by knitters, to signify, bring the cotton forward. I have only used it to express, bring the cotton over the needle, quite round.
Round the needle, means the same as the last term.