Looking at the disassembled flip key parts, you will see that the blank key blade is held into the pivot mechanism by a small roll pin. To get started you need to punch out the roll pin.
Take your time and be careful not to damage anything. Using a proper punch and small hammer, it came out quite easily. Since you're looking at this post, that means you intend to modify your donor key blade to fit into the housing. If this is the case, then you will not need the blank blade. I would suggest keeping it just in case something goes wrong in the modification process. The next step is to cut the valet key to fit into the flip housing. This is the tricky part...
I started by tracing the outline of the key blank onto the valet key. The valet key won't be able to be quite as long as the blank, but you should try to make it as long as possible, or the flip housing won't fit into the ignition area of the car. After it was traced out, I mounted it in a table vice and carefully cut/shaped it using a Dremel and a high speed cutoff wheel. This was not real easy, but I took my time and it turned out great. If you have more time, hand files would probably work just as well for this.
When I did it I took the pivot mechanism out to the garage with me and kept doing test fits while I trimmed it. The key is to take a little at a time until it fits perfectly. Then cut the slot for the roll pin very last. You want this to be in just the right spot to hold the key tightly. Once it fits well, push the roll pin back in (I used the punch/hammer and gently tapped it back into place).
If the modified blade fits snugly into the pivot mechanism then congratulate yourself because the hard part is over! The rest is just re-assembling things and is quite easy.