You'll decrease 1 stitch at the beginning and end of the same row and every other row after that the stated number of times. If it doesn't mess up the pattern, I would do the decreases one stitch in from the edges (on the 2nd and 3rd stitches from each edge). Did the pattern state how many times to do decreases at each edge every other row? Let's pretend it says 8 times. Then you will do a decrease at each edge, every other row, 8 times. This would mean decreases on rows: 2, 4, 6, 8, 10, 12, 14, and 16.
After finishing the every other row decreases, work 3 more rows. Then on the 4th row, and every 4th row following, decrease 1 stitch at each edge.
If you restart counting rows, this would be rows 4, 8, 12, and 16.
When a pattern says "every __th row", you wait until you get to that number row before you begin the decreases. So, every 3rd row means decreases on rows 3, 6, 9, etc.