Lion Brand site gives the following explanation: the turning chain at the beginning of the row, takes the place of the first stitch of the row. So, after working the turning chain, you will not work another stitch in the first stitch. And when you come to the end of the row, you will treat the turning chain as a stitch and work in it. For the single crochet, the rules change. The turning chain worked at the beginning of a single crochet row does not count as a stitch. After working the turning chain, you will also work a single crochet in the stitch below the turning chain. You will not work in the turning chain on the return row.
Also, in single crochet you chain 1; half-double crochet you chain 2; double crochet you chain 3.