My dear friend, Chris Schaefer, taught me some wonderful speed piecing techniques as well as this nifty way to pick up squares all at once. She's also the person who taught me to keep sewing onto a little scrap fabric tag rather than cutting the thread each time. Not only does it save time and effort, but also prevents threads getting knotted up on the backside of the fabric.
Now to begin machine piecing the baby quilt: Once all the squares are laid out in place, turn all squares in vertical row two face down onto the squares in vertical row one.
Pick up the pairs of squares starting at the top and keeping the first two on top of the pile. Put each succeeding pair under the one before it. Chain piece the pairs in this row together.
Pick up vertical row three beginning with the top square and always putting the next square underneath.
Open the first pair you sewed together and sew the top square in the pile to it, then, chaining it to the next block, sew the second square to the pair below and so one until you reach the last pair.
Pick up row four and sew.
Continue through the final row, making sure to keep the whole thing chained together.
Press (as in DON'T IRON!) all the seams in the top horizontal row in one direction, then press the seams in the next row in the opposite direction.
Match up seams and pin. Sew rows one and two together.
Press seam down. Press row three seams opposite to row two seams and sew that row to the first two.
Continue on until all rows are sewn together.
Press well on the back side.
Coming in Part 3: How to make borders that don't ripple.