After doing this I found that the pattern used a C hook, so use the smallest hook possible to get the puffier sts shown in the pattern photo. I did the extra yo indicated in puff st directions below to make mine a bit puffier.

My pattern translation to USA terms is below, possible with the help of Birdlebee’s notes. See the pattern for round-by-round photos.

Puff stitch (ps): (Yo, insert hook into st and pull up a lp) 3 times (4 times for puffier st). Yo, pull through 6 lps (8 if yo 4 times) -- one lp left on hook. Yo and pull through both lps.
Puff stitch shell (ps-shell): (ps, ch 2, ps, ch 2, ps) in st indicated.

Instructions show only what sts belong in each round. In other words, a rnd will not have the directions to continue to the next in a specific end st or beg st. Beg and end sts are variable, depending on individual color changes and can be determined according to personal preference. I chose to fasten off yarn and beg each rnd in the corner sts.

Ch 4 (last 3 sts count as dc)
Rnd 1: 2 dc in first ch, {(ch 3, 3 dc) in same ch} 3 times, ch 3, sl st in 4th ch of beg ch-4 to join.

Rnd 2: (Sc in any ch-3 sp, ch 1, ps-shell in 2nd dc of 3-dc grp, ch 1) 4 times, sl st in 1st sc to join.

Rnd 3: {(3 dc, ch 3, 3 dc) in any sc (corner made), ch 5, sk ps-shell} 4 times, sl st in top of beg ch-3 to join; fasten off.

Rnd 4: {Sc in center puff of ps-shell from rnd before the last one (enclosing ch-5 from last rnd), * ch 1, ps-shell in center dc of next 3-dc grp, ch 1 * , sc in ch-3 sp, rep bet * and * once} 4 times, sl st to 1st sc to join.

Rnd 5: {(3 dc, ch 3, 3 dc) in corner sc, ch 5, sk next shell, * 3 dc in next sc, ch 5, sk next shell * , (rep bet * and * as necessary across to next corner)} 4 times, sl st in beg dc to join.

Rnd 6: {sc in corner ch-3 sp, ch 1, * ps-shell in center dc of next 3-dc grp, ch 1, sc in center puff of ps-shell from rnd before last (enclosing ch-5 from last rnd), ch 1 * , rep bet * and * as many times as necessary across to next ch-3 sp} 4 times, sl st in beg sc to join.

Repeat rows 5 - 6 until square is desired size. To finish with a straight edge, end with an odd-numbered round.

See Birdlebee’s notes to see her option to continue border.

Made a sc border after a row 5, then another sc border to firm up. (43 sts + corner per side)