Australian Red Cedar top that has a few flaws but they are either outside the body shape or will be easy enough to hide.
Anyway, I use a shooting board and a small block plane to get the edges light tight. I'm getting better at it, and this one took 12 minutes. I prop both outside edges up and then stretch some tape across the joint. When the top is forced down flat, the tape pulls the joint together nice and tight.
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Get the hide glue nice and warm then close the two halves up like a book, with the tape to the inside. Spread glue on the edges, then lay the two halves down on a marble slab. Give the squeeze out a quick wipe off and then lay another piece of marble on top. Simple as

Note that I've got some sandwich wrap on the bottom side to I don't glue the top to the marble, and have some packing tape on the uppermost slab for the same reason.

I picked up the marble from the local tip shop. They've got heaps of off cuts from kitchen manufacturers. Only cost a couple of bucks and they're handy for all kinds of things in the shop.
You pros with dozens of instruments under your belts probably have a method that works better, but newbies might want to give this way a go.