Everybody does it a little different - kind of like chili or gumbo. Can't say one way is right or wrong, other than the fact that my way is right and your way is wrong!
This is how we generally do it, more or less:
Fill the large pot half full with fresh water, place on cooker, and start the fire. Place the lid on the pot and bring water to a roling boil.
While you wait for water to boil, rinse the crawfish with fresh cool water until draining water is clear. You do not need to purge them with salt. Rinsing will do just fine. But if you want to add salt, no biggie. Just remember that your seasoning has salt in it as well and be careful to not oversalt.
Add liquid seafood boil to water. Use what the label says to use for this part of the cook. Let the boiling water mix it well for a minute or so. Turn the heat down to about half after you get to a good roll and are well mixed on the seasoning.
Drop in all onions (halved), the potatoes, bay leaves and fresh garlic. Let this cook, keeping an eye on the potatoes. (Check for doneness by stabbing with a sharp knife or fork. If it goes in easy, it is cooked. Hint: Do not overcook potatoes, slightly undercook them because they will continue to steam and cook in the ice chest. You don't want to end up with mashed potatoes. Well, maybe you do, but I don't. Cook them until you can push a fork in and it meets resistance about 1/3 of the way through.) If you want to add sausage (I recommend it), do it here as well. Doesn't have to be andoulli - pretty much any good sausage is going to be awesome after being boiled in the mix.
When the potatoes are almost done, add the corn and mushrooms. Mushrooms are done when they are tender through, corn is done about the same amount of time. After they have cooked, place the vegetables in a small clean ice chest .
Turn the heat up on the burner. Add more spice to the water - you want about 2x what the label on your bottle says you should have. Add the lemons (halved) and squeeze the juice in the water. Then add the lemons to the water. When the water comes to a boil, place the crawfish into the basket and put the basket in the pot. I've also added honey at this point. Put in your butter here.
When the water comes back to a rolling boil - keep a very close eye on this part (time it) - let it boil for 2 minutes and turn off the fire. Let the crawfish soak for a few minutes (2 or so) and then remove. Hint: Kill the boil by adding cold - a frozen jug works well, just want something that is a heat sink that won't alter or dilute the mix. Then let the crawfish soak. Most of the crawfish will sink to the bottom and fill with spicy water.
Remove the Crawfish from the pot and pour into an ice chest and let steam for 5 minutes. This is where the argument usually starts - to dust or not to dust. I actually like a light dust because in order to eat crawfish, one must use their hands. The dust gets all over your fingers and adds a touch of seasoning to the meat while you are peeling. If you only season here and not the boil, you suck at life. Use more or less spice to your taste.
Enjoy - serve with cold beer and good friends. Hard to beat a good crawfish boil and gathering.