The gear and processes I have worked out steal ideas from many sources, primarily NWKA. Please keep in mind this is the way I do it. It does not mean I think you should do it my way. I do think there are some good ideas here that are worth considering, but in no way do I believe my way is the only right way. In the end, whatever safely and legally puts crab in the boat is good method.
Since the traps collapse and lay flat using a rigid bait box defeats the folding advantage. Bait should be placed in a mesh plastic bait pouch.
We have the trap and the bait pouch, and we can carry the traps on the yak. Now we need bait and a way to deploy and retrieve the traps. The gear used here to organize the lines is adapted from the BSteves Anchor system (of NWKA fame). The heart of the line management is a cheap plastic extension cord winder available at many hardware stores.
You may have heard canned cat food (a fish flavor) works well as a bait. It does. Just stab a dozen holes in the top of the can with your water knife - you do have a water knife?. I've experimented and found no discernable difference between chicken legs and cat food. However, what to do with the can when you are retrieving your gear? A chicken bone or fish carcass can just be tossed overboard. A rank, stinky cat food can needs to be retrieved and disposed of on land. Cat food is for cats - and maybe dry boats.
If you are in a pinch for bait, consider flounder if you have them in your area. A jig, some Berkley GULP! Saltwater curly tails and you have crab bait, even if you have to handline. Keep the small ones, cut into pieces suitable for your bait pouch, and freeze.
My personal convention is the "down" ends have leash snaps and the "up" ends have loops. The down end of the mainline has a brass leash snap to connect to the link on the trap harness. About 10' from the other end is a weight loop, and at the surface end is another simple loop. An 8 ounce ball with attached loop is looped through the weight loop on the main line to keep extra line submerged and clear of passing boats. I also carry two 25' line extensions for when I want to deploy in deeper water. They are just like the mainline only shorter, leash snap on one end and loop on the other.
By law in Washington state a crab float must be red/white and have your name and address printed on the float. Here is a float with a short length of line ending with a leash snap. Some folks use a flag on a rod for increased visibility - not a bad idea I have not yet incorporated but will.
To load the mainline on the reel just loop the leash snap around the spindle and snap to the line, then wind evenly onto the reel. The second mainline is snapped to the loop on the first mainline and wound evenly on the reel. Wrap your extension lines neatly and securely for stowage on the boat or PFD.
At your location, the first thing to do is attach the float to the trap. This will likely not keep the trap from sinking but should give you some time to snag the float or line should it go overboard - yes, again, the voice of experience. Generally, I bait and erect the first trap on the beach. However, for a collapsed trap I lift it off the securement and swing it onto my lap and erect it, or I swing around, straddle the yak facing backward and erect the trap. The rougher the conditions the more likely I am to swing around backwards. Now the mainline is attached, the buoy removed, the trap swung overboard, and dropped. Holding the winder by the center handle, the falling trap simply pulls the mainline off the winder. When the weight loop is free, the weight is attached, and tossed overboard. When the mainline end loop is free the float is attached and thrown overboard. Immediately mark the location on your GPS.
Use your GPS to locate your float. Remember tides can pull your line to the other side from where you deployed, and strong currents can drag traps some ways. Once located check that it is your float. You will want to pull the trap from the upwind/upcurrent side of the yak - explanation shortly. Snag the float and pull it on board. Now throw the float over the other side of the yak. Now start hauling in line. Either collect the line in the boat and periodically toss a few coils over the other side or pull the line in such a way as to drop it on the other side in one motion. Which may depend on your body type. The combined wind/current will pull the float away from the yak and you will be trailing a line 100-125' long on the other side of the yak. If you are in a congested area this may not be safe. Generally responsible boaters give kayaks a wide berth, but occasionally there are exceptions. Use your judgement. This method of retrieval line management is courtesy of a Hobie yakker, Zee, also of NWKA fame. When the trap is at the surface grab it and swing it aboard. I usually place it over the live well where it is stowed for transport. Carefully drop or lift the side of the trap toward you and sort your catch. Keep the keepers and toss the others overboard. Rebait if redeploying and check that you have not drifted into deeper water than your main line can handle. Yes, that is the voice of experience. Drop it back down on the same side you pulled it up. You want the trap to drop straight down. If you drop it off the side where all your line is trailing it will swing to the bottom more like a pendulum, striking the bottom at an angle. This can damage your trap. The trap should hit bottom before the float reaches your kayak. If not, PULL IT BACK UP and relocate as you have drifted into deeper water.
Some folks use a bucket for line management, pulling in the line and collecting it in a bucket or tray in their lap, much like some fly fishermen use for line management. This method works well. I tried it a few times, but I have no use for a bucket or tray other than collecting line, and then you need to stow and carry around the bucket. I already have enough shit on the boat.
At some point you will retrieve the traps and bring them back to land. Collapsing the traps for stowage is the reverse of erection, and rather than redeploying the line simply wind it back onto the reel. Remove the line weight when encountered.
Some people steam, but I boil my crabs. Bring enough salted water on high in a big enough pot to a vigorous rolling boil. Some people throw in Rex Crab Boil and other seasonings. The cold crabs are sedate enough for safe bare-handed handling, but DO NOT dawdle when holding them in the steam before dropping them into the water. They can wake up surprising fast when they feel the steam heat. An amazing thing happens immediately after dropping them in the water, their shells turn bright red in a wave of color starting at the edges and moving into the center. It's all over in just a few seconds. I let the water return to a boil and boil for 30 minutes. Others suggest less time. Immediately remove and rinse in cold water. Let them cool a bit until they are comfortable to handle, then clean.
Now the icky, educational part, cleaning. Remember, these are big crabs, the Washington State minimum size limit is 6-1/4" across the widest part of the shell. I've seen crabs 8" and 10" across! These ain't no tiny, wimpy East Coast, metrosexual Blue Crabs! These be manly crabs! I have found no better description of cleaning a mighty dungeness Crab than this description from Instructables.
Some comments on the cleaning description from Instructibles. The yellow-greenish goo is coagulated hemolymph, blood, and it is commonly called "crab butter". Some consider this a delicacy and there are recipes around which use it. Save the crab butter if you are so inclined. I don't, but then, I don't suck the heads of mudbugs either.