The hardest part is usually getting the bindings off, since they're usually riveted on.
Before you do that, put the shoe you want to mount in the binging and find a way to mark it so that you can put it in the exact same spot with the binding off. I usually put some marks on the decking to get the shoe lined up L-R and front to back.
After that, get the bindings off with as little damage as possible. This will include removing the front cleat off of the bottom of the shoe. There should be somewhere between 2 and 4 rivets in the cleat, and the holes that those rivets were in are where you'll have to mount it.
Next step, line the shoes up and secure them with a rubber band or something so the shoe is where you want it to sit. Through the rivet holes, use some sort of marker or pen to mark the sole of the shoe you'll mount, so you know where to drill the holes.
Remove the shoe, get a drill and drill through the sole of the shoe as straight and neat as possible (try to use a drill with an ever so slightly smaller diameter then the screw you're using).
To secure the shoe on, you'll need some screws (or bolts, or whatever you call the threaded kind with a flat end, not pointy) that are approx 3-4" long, washers and lock washers of the appropriate size, and some patience. Try to find screws with as flat of a head as possible, because if the screw has a big bulky head, you're really going to feel under your foot when you put the shoe on.
When you put the screws in the shoe, there should be a flat washer on the inside of the shoe (to keep the screw from pulling out the bottom). Once you get all of the washers and screws all the way through your shoe, line the protruding screws, put the screws through the rivet holes in the binding. Lastly, thread the screws through the cleats, put on the lock washers, and then a good solid lock nut to hold it all together.
From the inside of the shoe to the bottom of the snowshoe, you now have
Flat washer
-----------
Midsole of the shoe
-----------
Snowshoe binding
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Snowshoe cleat
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Lock washer
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Lock nut
With a 3-4" screw going through the middle to hold it all together.
Now as for the details of how mane screws to put in (some cleats have 4, some only have two, some have more), thats up to you. More screws means a more secure hold onto the snowshoe, but the more screws you use, the harder it is to get them all to line up right, and if the screws are lined up crooked, the shoe will be crooked on the snowshoe. Another side note, some people find the decking to be a bit floppy without the binding on top. If that is the case, you can take the base of the binding (if it has one) and add that between the shoe and the snowshoe to give you a little more solid platform.
I think that about covers it. Take it slow and be careful, and you'll end up with a wonderfully secure and light snowshoe that requires no bindings whatsoever.