Here I've transcribed my father's crawfish recipe. The original link still exists (Dad's crawfish recipe), but he hasn't updated the site in almost a decade. This page will be my copy of it.

Crawfish pot ready to serve!

Boiled Crawfish

Tools

Rapid gas (propane) burner
60+ quart/liter boiling pot with matching lid
colander/strainer (pot and colander usually comes as a single kit)
large washtub (for soaking/purging crawfish)
3-4ft (100-120cm) wooden cooking or boat paddle

Typically the burner (with regulator and hose for connecting to a portable propane tank) and the pot/colander kit can be bought together. Amazon has many options, and you may be able to find these at your local hardware or sporting goods store.

For the large washtub (at least 60qt/L), I actually have two identical plastic washtubs with rope handles that fit inside each other. I drilled holes in the bottom and sides of one of the washtubs, to make draining the water out easier. In Louisiana many hardware stores sell these pre-made, but hardware stores usually carry these (they may be labeled solid, large laundry baskets).

Ingredients

Seasoning Mix

Dad usually buys the dry seafood boil mix from a commercial supplier., typically coming in packages for one whole sack of crawfish. Some local seafood shops also prepare their own. The alternative is the cloth bags of dried spices to which you add salt. As a last resort, you can buy the liquid spices, but this usually results in a rather bland boil, unless you really spice it up a with more cayenne and salt. I have recently been using the dry spice mix (includes the salt) from Louisiana Fish Fry products in Baton Rouge, LA (1.800.356.2905). Zatarain's makes good stuff too.

2020 Update: This Spring, due to COVID-19 quarantining/social distancing, April and I decided to make several (8 total) small 4lbs batches of crawfish in our kitchen on a weekend in March. We tested several types of seafood boil mixes, including Old Bay seasoning, Zatarain's Crab & Crawfish Boil dry mix, Louisiana Fish Fry Crawfish Boil dry mix, Zatarain's cloth crab boil spice bags, and Zatarain's liquid boil. The clear winner was Louisiana Fish Fry dry mix, it had the perfect balance of flavor, and it tasted the most Cajun of all the spices we tried. Old Bay was the worst, followed by the Zatarain's cloth bags. Both of these were pretty bland, and required more salt and cayenne. They also made the crawfish look dirty with all the spices clumping on them. The Zatarain's liquid boil was the surprise, it was pretty spicy (though lacked any other flavor to speak of). If you’re preparing the crawfish for a mixed crowd (where some folks can't handle spicy), Zatarain's standard Crab & Crawfish dry mix wasn't as spicy as the Louisiana brand, but that may have been because the Zatarain's was expired (the label on the plastic jar said it expired in 2018). We did not try the Zatarain's liquid Pro Boil. Maybe next year!

The Rest of the Stuff!

This is for one sack (30-40lbs/13-18kg) of live crawfish.

12 medium-sized lemons, halved and squeezed into the pot (substitute two cups/500mL white vinegar if you don't have lemons)
12 whole onions, halved (don't peel off the outer skins)
4-6 whole garlic heads, halved to release flavor (again, don't worry about peeling the garlic)
2 bags small red potatoes
8-10 ears of sweet corn, shucked and halved
Seasoning mix (see above)
Additional ground cayenne pepper to taste

Optional Ingredients

one cup/250mL of whole cloves
andouille (smoked sausage, I prefer Conecuh Sausage, original or hickory)
whole artichokes (the whole flower, not the canned hearts!)
whole mushrooms
Brussels sprouts (trust me, this is one of the best ways to cook these!)
pineapple slices or chunks, if you're feeling adventurous!

Crawfish Preparation

Obtain a sack of live crawfish and keep cool and wet until ready for the boil. Prior to boiling, empty the sack into a large container (washtub). Rinse thoroughly and drain. Do not leave the crawfish in water as they will die because of lack of oxygen. Some people add salt to the water to "purge" the crawfish. This is fine but do not leave them for an extended period in salt water and be sure to boil them immediately after purging since crawfish are freshwater animals. (Dad says he read of an LSU study [citation?] which says that purging crawfish is no longer necessary because they are now largely farm-raised, and hence aren't full of mud like wild ones would be).

Set up for Boiling

Set up a large (60qt/L or greater) pot with strainer/colander well away from the house outside on a rapid gas burner. This is done because of heat, gas flame, and mostly the pungent aroma of the cayenne-spice mix. Fill 2/3rds with fresh water and start burner on high heat. Add spice mix (and salt if necessary) and lemons. Additional cayenne pepper and cloves may be added at this time. Bring to full rolling boil. Add potatoes, garlic, and other vegetables and sausage (except the corn), stir. Return to a full rolling boil. Let potatoes cook for about 5-10 minutes (depending on potato size). Add corn and let cook another 5 minutes.

Boiling the crawfish

When the pot reaches a rolling boil, put half the sack of crawfish (15-20lbs, if your pot is 60-80qt), or the whole sack (30-40lbs, if your pot is 120qt) . Stir gently (Dad uses a wooden boat paddle, I use one specifically designed for cooking like this). The crawfish will sink at first. Put the heat on high, cover, and return to a rolling boil. Cook the crawfish for about 5-8 minutes. Be careful not to overcook! The way Dad tells is that when the crawfish are cooked they will begin to float and sometimes cause the pot to overflow (Dad sez,"Dat's another reason why dem crawfish are cooked outside, yeah."). When most of the crawfish are floating, it's time to turn off the heat. Do not remove them from the pot just yet, because now comes the most important part: let the crawfish soak up the spices. After turning off the heat, leave the crawfish to cool in the pot, soaking up the spices. Dad leaves them in the pot for up to 30 minutes or until they start to sink again. When they sink again, they are ready to spread on the table to finish cooling.

Enjoy dem mudbugs, spicy corn, potatoes, and other veggies!