If you find that small fused sections stick to your sewing machine bed, simply put tissue paper under them. 
.
Gently tear off the tissue before completed sections are fused together.

These tools go a long way in making machine appliqué easier.  I use:
.
Non-stick teflon pressing sheet
(many shops carry these)
.
Stiletto (or awl)
.
Light box (available in craft shops and some quilt shops)

Fun to shop for and fun to use!

The secrets of appliqué are available to all quilters.  There are different styles of appliqué that can be done with Quilt Poetry patterns, depending on the skill level and desire of an individual quilter.  These patterns can be hand or machine appliquéd (or any combination of the two!)

Personally I choose to do raw-edge fused 

machine appliqué.  I use a triple straight stitch and zig-zag blind hem stitch, and I have fun using variegated and metallic threads!  (Phoenix and Mask quilts are particularly amenable to variegated threads.)  The bottom line is, you can do this!  Choose a technique that's right for you.  It's easier than you might imagine -- but the results will look absolutely amazing.

While Quilt Poetry appliqué can be done by hand, here's my technique for using a machine.  Don't forget to check your local shop for information and classes!

Below, I've used Floral Meditation as an example.

Earlier I'd fused this small section together using fusible web.  Fusing on a non-stick teflon pressing sheet lets me peel the completed unit away in one piece.  ... All ready for interior stitching!

Later, you'll see how this small and easily made piece fits into the larger whole.

And ... to keep from having to raise the presser foot every few stitches to pivot the piece, lower its pressure setting, if your machine allows it.

Check your machine's manual for instructions for lowering the foot pressure, and try it on a practice piece before proceeding on the project.

The pattern is under the non-stick pressing sheet, and I begin to place the petals on top.

The pattern and pressing sheet are pinned to the ironing board so that neither one moves during placement. 
 

I like using a stiletto to help guide the piece accurately into position.

The non-stick surface of the pressing sheet will allow the completely assembled flower head to be easily pulled off later as a single unit. 

The fabric will retain its fusible, adhesive quality when removed from the pressing sheet.  The entire piece will then be ready to fuse to the background fabric, using your iron.