Select yellow rose: 
The fastest method is to use the Magic Wand to select the background, the Marquee tool to add as necessary,
and then invert the selection.
Change the mode of the brickwall to Greyscale: This is very important! GIFs use indexed color which is not full-spectrum. If you do not convert to greyscale you will end up with bad artifacts in the remaining steps.

Copy and paste yellow rose into the brickwall GIF: This automatically converts the mode of the rose to grayscale.
If we were really concerned with quality, we would have carefully converted the rose to grayscale in the original file
using only a couple of channels judicious sharpening and cleaning up and then selected more carefully.
We would have gotten a much better looking grey rose.
Defringe the new layer:
This only works for layers like this where something is pasted into a newly created layer with areas of transparency.
Defringing works on the edges trying to eliminate unwanted fringes of a different colored background.
This happens a lot when selecting a dark object on a white background and pasting it into a dark background, for example.
Defringing will take the colors adjoining the "fringe " and recolor the fringe to match the interior colors.
Obviously you only want to do this in small doses.
Under the Layer menu choose Matting at the very bottom and then Defringe [set it a about 3 pixels for this project.
For high resolution images you may be defringing 10 pixels or more.]
Move the rose layer to the position seen on the composite: You need the Move tool for this operation. Type V to access the move tool and then just click on the rose and drag it into position. You can nudge it into a more perfect location by using the Arrow keys.
Select the background layer and darken the wall: You will find several options to do this under the Image menu out to the right with Adjustments. Save first, and then just experiment with Levels, Curves, Variations, or Brightness -- whatever works. If you mess it up, just revert to the state you just saved.
Save the new composite under the name [yourname]composite.gif: and attach it to an email for grading.
If you are still confused about this process,
here is a link to another defringing tutorial.