I've written a book about this (now out of print). Don't do it one block at a time--joining is awful. Divide your quilt into strips. Batt and quilt them in a frame similar to a needlepoint frame. For example. your quilt is 5 blocks wide by 7 blocks long. Piece the top in 5 strips, each one block by 7. Cut out the batt to fit each long strip. Cut the backing about 1 inch larger on all sides. Baste all three layers together as in conventional assembly. I use a serpentine row of basting that is 2 inches apart for the first and last rows for about 12 inches and in the body of the strip the rows can be spaced 4 inches apart. Put it in the frame and quilt. When two strips are quilted, they can be joined. Lay wrong side up on a table. Fold the backing and backing out of the way and pin the top seam allowances together. Stitch together by hand (machine piecing would catch the batt). Once the top seam is pieced, butt the batt edges together and whip stitch the batt together. Don't overlay, but trim excess batt away. If you don't do this the batt may pull away from the seams if not outline quilted. The final step is to join the backing. Lay one side down (trimmed to about 1/3inch) and then lay the remaining side over it, turn under the seam allowance and pin in place. I reach under and feel the top where the seam allowance is that you just joined so that the backing seam is directly over it. Use a blind stitch of your choice to stitch the backing in place. Go into the batt with the needle, but be careful that the top is not caught. Keep adding strips until the entire quilt is made. I've made king size quilts this way and have taught this method for 20 plus years. From the top the quilts look identical to any other top assembly, the only difference is that on the back you have a seam where each strip is joined. Just as strong, only a few more backing seams. Good luck--go for it! By the ways my book was titled Quilt-As-You-Go.
SandyQuilter