The photo above shows the dishcloth facing upright, with the outside edging round started, working along the left-hand side of the cloth. When you are crocheting, you will have the piece turned so that the side you are currently working on is facing upright. I turned it for the photo so that you could see and clearly understand, in relation to the upright piece, what the crochet instruction means when it says to "work down the side of the piece" or "crochet along the left-hand side of the piece".
The outside round is worked around the stitch on the end of each row. If there is a single crochet at the end of the row, the hook is inserted either partway through the single crochet stitch or between that single crochet stitch and the next stitch (use the way that gives you the look that you like best), then the yarn is pulled through and completed as a single crochet (or completed as the type of stitch that the pattern calls for).
If there is a double crochet, treble crochet or any longer stitch at the end of the row, the hook is inserted between that edge stitch and the next stitch of the row, then the yarn is pulled through and the stitch to be completed is made around the post of the double or treble stitch. More help for this technique: sc around post, step-by-step photos
The photo shows my Pointed Edging Double Crochet Cloth , which you can print out for free from that pattern page. The photo here shows the cloth before the pointed edging is added.
Written by Sandi Marshall, copyright 2008 by Sandi Marshall, licensed to About.com, Inc.