I've made a number of quilts of 4.5 inch squares. You *can* keep them lined up. Make strips of sewn-together-squares, being careful to keep the seam allowances uniform when sewing. Then, when sewing the strips together, gently stretch whichever piece is going to come up short to ensure the corners will align. And remember, they don't have to be perfect, just close enough to look good. And always remember "the underarm rule" - Anyone who examines my underarm to see how well the seam lines up deserves whatever they get!
There are a number of ways to make the pieced top.
If you want to make the quilt quickly, use "strip piecing". Cut a number of strips of fabric with the width being the desired square size (including seam allowances). Sew the strips together along their long side to make a striped piece. Then, cut it in the other direction, to make strips of squares, again, with their width being the desired square size (including seam allowances). Make several striped pieces in this manner and cut them into strips of squares, then sew the strips of squares together to rapidly assemble a pieced block.
If you want a method that gives you more control but takes a little longer, yet is still fast... Sew one square to another. Then, without cutting the thread, pull them out an inch, and start sewing another pair of squares. Repeat until you have a number of pairs of squares sewn together and connected by a chain of thread. The number of pairs should equal the number of rows you want in the quilt. Then, go back to the first pair and sew on a third square. Repeat the process, attaching a third square to each pair, not cutting the thread. Add fourth squares, etc, until you have strips of squares sewn together, all attached by chains of thread between the seams. You can then quickly and easily sew the seams in the other direction, and you've got your grid. The purpose of not cutting the chains is that it keeps everything neatly in place until you're ready to sew the other direction.
YET ANOTHER way is called quilt-as-you-go. Make your strips of squares, not chained to each other. Cut the backing fabric into strips as well. Cut the *batting* into strips. Assemble one row of squares, batting, and backing into a sandwich, and overcast all around the edges or run it through the serger. This mushes down the edges and makes them tight. Then, lay another strip of squares against the squares of this assembled strip, right sides together. Place a strip of batting on top. Place a strip of backing underneath, right sides together. Stitch it down along only one long side, and then overcast it. Or just serge it in the first place. Pull the first strip out, pushing the backing, batting, and strip of squares you just attached to one side. Then, overcast down its open long side. Repeat until you have a quilt. (I made a complete baby quilt from uncut fabric to finished quilt in 90 minutes this way, and it sold at auction for $150 for charity on TV that evening.)
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