I am getting ready to do my first applique block. I am a new quilter. The applique is of three butterfly templates. After choosing the material I decided that the butterflies really needed embroidery embellishment. Now the question is when do I do the embroidery? Before I cut them out or after they are fused to the background? Thank you for your help.

Because to fuse, you have to use heat, it is always best to do your fusing, extra stitching to background, perhaps even the completed quilt quilted before doing your embellishing. <wave>

Trying to get the picture. You have three butterflies that you are appliqueing to a background, using fusible web .. and you will then stitch the edges down? (around the fusing)
and, you want to embellish the butterflies with embroidery (by hand?) ... if it is simply thread embroidery, you can do it as soon as you have the butterflies attached to your background.
Have you invested in a teflon sheet?
I didn't see that you mentioned how many blocks you will be making, but you will want to iron the blocks as you join them. Since the iron will be hot, a teflon sheet placed over the top of the embroidery and fusing should protect the embroidery.
Is that a better answer for your question? <wave>

I haven't invested in a teflon sheet. That's an interesting piece of knowledge. Thankyou. I am of course learning as I go.

It's just a single block that will be a part of my learning quilt. So far I have a, "birds in flight" and "4 Diamond" blocks for the paper piecing lesson, 4 "Bowties" and a "cobblestone" block for the piecing lesson, and now I'm on applique with the butterfly block. All in all I'm looking to complete 15 blocks of all different techniques and then add sashing to frame each one and then do a boarder. I'm thinking of a finished size of 57" x 38" my colors are christmas red, dark steel blue and harvest gold with black sashing and boarder.

Since I'm using cotton embroidery thread do I really need to protect it when I iron? I didn't know that. When using the silk definitely but this isn't the silk thread.

I'm not sure about the DMC cotton ... I iron with steam, and there is always that color running thing sometimes under the hot water of steam.
If you are thinking "embellish" ... I am thinking you know more about how safe the elements are than I do <g> ... I never think embellish LOL <wave>