There have been lots a great tips offered, some I will probably try
myself. However. it looks like you use paper and plastic in your
pieces, so some of the tips just wouldn’t work for you in this
I use the blue painter’s masking tape, taking a few strips of it and
wrapping them criss-cross around the pieces to hold the work
together securely. With flat work, this is fairly easy.
But before you tape the whole thing together, drill all the holes in
the top piece on it’s own. Then do the taping. The holes in the top
piece will act as pilot holes, so you will get precise placement of
the holes in the other pieces. Drill through one pilot hole into the
rest of the piece, install that one rivet before drilling the rest
of the holes. The first rivet will hold your work together securely,
allowing you to more easily drill and rivet the rest. It is easiest
to drill each subsequent hole and install the rivet one at a time,
before moving onto drilling the next.
I use an old cordless drill to drill the holes. A good tip to keep
your drill bit from wobbling off the exact spot and moving your work
out of alignment, even with the pilot hole there, is to use a center
punch. It’s a carpenter’s tool you can find in any hardware store.
Choose one with a nice fine point. While your work is taped
together, insert the center punch through the pilot hole, lightly
strike the top of the punch with a hammer
(just once), and this will create a tiny dent. Rest the tip of the
drill bit into this little dent, and drill.
Good luck and have fun!