Step 1 - Placing Pieces
You may need to hold your stabilizer & backing fabric up to a window to see exactly where the pieces go. Look at your pattern and the pieces you have to applique and decide which should be attached closest to the backing fabric and which will be attached on top of those. Pin the first piece in place.
Step 2 - Stitching
The next step in appliqueing a quilt block is the actual stitching. There are several ways to stitch around the edge of the pieces. I prefer a stitch that is nearly invisible.
The front of your quilt will have the tiniest stitches along the edges of the fabric pieces. The back side of the fabric will seem to have little dashes going all the way around the pieces that you've stitched down.
I'm going to send you to several other sites that explain it better than I can. Or you can probably find a book at your local library that will detail the actual stitching process.
Learn to Applique has the best instructions for the actual hand sewing of the applique pieces. It gives directions for turning, clipping seam allowances, and pressing, etc. The site also suggests two ways to use freezer paper. The freezer paper method I've described is the one she calls "Now the Method I Use" at the very end of the webpage.
Another source for more information is Standard Hand Applique Stitch where you can see another drawing and explanation.
Or this video might be helpful to you.
Step 3 - The Tiny Pieces
Sometimes you will find that there are some very small pieces to be appliqued. You'll have to decide your comfort level in regards to the size for appliqueing. Often it's better to embroider the smaller pieces, and I think it's always best to embroider lines.
Step 4 - Finishing
You may find that you'd like to wash your block before sewing borders on it or sewing it into a quilt. You can do this by hand, gently, and then lay flat to dry. You may find that you'll need to gently press it when it's just slightly damp.
And you're finished! Hooray!
Other posts in this series:
"A is for Airedale" Quilt Patterns Available Now!
Applique an Airedale, Part 1 - Tracing the Pattern
Applique an Airedale, Part 2 - Auditioning and Choosing Fabrics
Applique an Airedale, Part 3 - Cutting the Pattern Pieces
Applique an Airedale, Part 4 - Stitching, Finishing
Applique an Airedale, Part 5 - Photos