Carefully cut out the pattern pieces you traced onto freezer paper earlier. Carefully, on the lines. It will seem like you have puzzle pieces because of all sizes and shapes.
Step 2 - Evaluating Layers
As you've been working with your pattern (and if you're appliqueing by hand) you may have realized that some pieces will overlap others. In the photo to the right I think you can most easily see that with the front legs on the right side of the photo. One front leg is attached to the dog -- it's the right leg. The other front leg -- the left leg -- is unattached. On the unattached left leg you can see the outline of the right leg. That unattached leg will be stitched before the leg/chest/head piece.
Look at the saddle/upper tail and hind leg/under tail. The hind leg/undertail will be stitched first, then the saddle/upper tail will be stitched on top.
Hold this thought while I tell you the next step or two. You may need to come back to this to look again.
You used freezer paper to trace and cut out your patterns because the wax on the underside of the freezer paper will melt and hold onto fabric when ironed.
Lay your cut out paper pattern pieces shiny side down (drawn pattern side up) on the front of the fabric you've chosen for each piece. Heat your iron to the setting appropriate for your fabric (probably cotton) and place the iron on the paper and fabric. Do not slide the iron, just press. Hold for about 10 seconds, then lift. Let the paper cool for a moment and check to see if it adhered. You don't need to work at separating the paper and fabric, you just need to be sure the paper doesn't easily lift from the fabric.
You can iron all your pieces at the same time or iron them as you go.
The paper pieces you cut are the exact shape and size of the finished quilt block.
When you cut the fabric around the paper pieces, you should cut 1/4" beyond the paper. That 1/4" will be turned under and you'll stitch along that edge.
But that's not always true in hand applique. Because of the layers I mentioned above, some pieces or parts of pieces can be cut exactly on the line. In the photo to the right you can see that one leg has 1/4" of fabric to turn on along only one side and the curve at the bottom. The fabric on the left edge was cut along the edge of the paper pattern. That's because another piece will overlap it and cover that raw edge. You can see that the other leg has the 1/4" of fabric all the way around its edge. All of its edges will be turned under (except the top where the body will overlap it).

Sometimes it's easy to see which pieces will be stitched first and have others overlapping them. Other times it's not so easy and you have to make a decision about how easy or hard it will be to do it one way or the other.
Step 5 Turning Under
The 1/4" of fabric around the outer edges of the pattern pieces will need to be turned under before they can be stitched to the background fabric.
Turn the fabric under along the edge of the freezer paper pattern and either iron it in place or finger press it (by scraping your using your finger or fingernail along the edge). Some pieces with tight curves may need to have a little glue from a water soluble glue stick dabbed into the fold.
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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