Cutting and glueing: YAY!! This is by far the coolest part. We get to see our pictures come to life, one piece at a time. The decisions that we have made in our desing will strongly effect the decisions we make now.
I just want to cover a few points before beginning to make things a little easier.
You will need to hold your blade as straight as possible to get a good cut.
Here I have drawn a piece of paper.

Right handers...you will want to make your cuts in a clockwise direction working around the outsides of your shapes. Lefties...counterclockwise. Stay on your lines! (Yes, you have to stick to the lines on this one) You can hold your blade straight to slightly leaning away from the paper and get a good cut.

In the picture above, the lines on the left and right of the shapes represent the cuts.
Below is an example of a bad cut. here the left and right margins are pointing up towards our painted surface and will result in white paper showing in the cracks between your pieces.
There will be times when you will need to reverse the direction of your cut in order to prevent leaning your blade in towards the piece you are cutting out.
I will make the eye of my toad in two cuts. ( I decided not to make those tiny pieces around the pupil in the design and will just make my pupil that much larger instead). the blue portion of the eye will need to be cut out first.
lay your design on the desired area of your swatch and cut it out. Righties...cut counterclockwise.... etc. Set this piece aside for just a moment. Next select the area of your swatches for the iris. The first thing you will need to do is cut out that missing portion...the pupil. Here is where you will reverse direction. After you have the center removed go ahead and cut the eye out of the swatches.
Because these two pieces will fit directly into each other we will have an easier time if we just put them together now and then glue them to the paper.
Take your design/pattern and lay it on your background so that the frog will end up where you want it. Next you apply some glue to the back of your cut out pieces (they should be together in your hand) and glue them in place. Carefully remove your pattern and place the collage under your really heavy book. I find that my glue has usually settled well enough by the time I'm ready to apply the next piece that I can just keep working one piece at a time. I've tried applying muptiple pieces at one time but have found it really doesn't work too well because the pieces are always in a hurry to curl. The eye is the only time I attempt two pieces at once. (Well, I suppose there could always be exceptions to the rule...)
Okay...got all that? Here is what my piece looks like with the pattern still in place.
And here it is with the pattern removed...
Kinda scarey lookin' isn't it!
the next piece I will cut out will be the upper eyelid. Because I have already cut the eye out from my pattern I will have one exposed edge to cut and then the sides with lines. It is important to cut the exposed edge first so that you can hold things down as long as possible without a floating piece of the pattern. Remember to keep your blade as straight as you are comfortable with and don't lean in towards the piece you are cutting. Now that you will be cutting an exposed edge it will also be important to keep your blade from going under that edge. That will result in your piece being too small. You'll notice the pattern lifting slightly if you go under.
In this picture I have cut out the eyelid and have placed the pattern back down on my collage. It is important to do this with every piece you glue in place so that you can properly line things up for that perfect fit.
Here in the picture below you can see a tiny line of blue showing next to the purple piece. This is the result of poor cutting and pattern slippage. I expect this will eventually happen with any piece so I'm not too worried. I will keep working in areas that still have a good fit and address this part later with the help of a transparency. (Yuck)

you'll notice I've lettered some of my pieces. I'm making colour decisions and don't want to forget later
As you choose your areas of colour aim for pieces that will work well together. If things are too busy it may be difficult to tell what your image is supposed to be. I always like my pieces to have a colour change within them. Sometimes it is subtle, like the same colour going from light to dark...
I'm working my way towards the right. I'm dieing to see how the hand will look. As you get to these outside edges of your piece you may be tempted to cut away some of the pattern as it does tend to get caught up on the pieces already in place. You will want to keep the integrity of your pattern intact so if you want to do some cutting away...don't go all the way to the edge.
Here I have cut away around the fingers...
Fixing bad spots:
To fix spots where the pattern is no longer fitting right, lay your pattern on the piece and then lay a transparency or other tracing paper over that and redraw the piece ...compensating for the error. You will need your permanent fine tip marker for this so that the lines don't wipe off while you are cutting. transparencies are really slick and hard to hold down to the swatches. You can try using some tape to hold it in place until you are done cutting.
If you have a piece that you've glued in place and you really want to change it out you can soften the piece with water and gently remove it. retrace the missing piece on your transparency or tracing paper and cut a new swatch.