Step 1: Start Sewing Your Block Pieces
Start sewing your pieces together, using a 1/4" seam but before you get to the end of the fabric, line up your next 2 pieces so that it touches the end of the pieces you are sewing.
Step 2: Continue to Sew, From One Set of Pieces to the Next
Don't stop or cut threads as you normally would if you were garment sewing. Don't reverse sewing or stitch in place to secure threads. Just keep right on sewing off the edge of on set of quilt pieces and onto the next set. This is how you "chain" piece. The quilt pieces will be all stitched as a chain and when you are done sewing them you simply snip the 2-3 threads between each set of pieces and then press.
Step 3: Pressing
In quilting, pressing is an up-and-down, lift-press-lift motion.
Pressing is important in quilting and doing it right takes practice - it's not ironing! You should not move the iron at all while pressing the fabric. In quilting, you press the seams either to one side of the stitching OR you press them open, but you never move the iron while you are doing this.
Pressing is not ironing - like you might iron clothes. For quilting, use your fingers to gently lay the fabric where you want it to be, then put the iron down slowly on the seam, letting the heat and the weight "press" the seam. Lift the iron.