Not turning work

When my shawl pattern says knit row then do not turn and begin next row, how do I do this.?

What pattern are you following? Can you give us the name or a link to it?
As a guess, it might be something like an I-cord particularly if the row is 3-5sts or so. In that case you keep starting the row as stitch one without turning.

It is the blue sky window silk wrap. Thank you.
It may be that you leave a yarn tail and knit across the row leaving a long tail at the end of the row for the fringe. Then you start again at the beginning of the row with a new strand of yarn.
So rather than tuning to the back you are always working across the front of the wrap.