Removing the iguana from the snare
As stated before, you should practice releasing the snare before catching an iguana. Iguanas have teeth and can bite although none have ever tried to bite me. They will also try to whip you with their tail.
I grab them behind the head and under the front legs. Sometimes they are calm enough that you can hold them on the ground to release the snare. Usually I have to lift them off the ground and at that point they are almost always totally calm. Iguanas over four feet long will be more difficult and more aggressive you may want to call for help. In some locations, like near a seawall, the iguana may be hanging from the snare. Although the body may be limp and lifeless, don’t assume they are dead. They usually come right back to normal after a few minutes.
I grasp the cable about ½ inch in front of the locking slide and push the cable into the hole. You may have to wiggle the cable a bit to get it to go straight into the hole in the locking slide. You can then grab the slide and pull the snare to the full open position. You may find it easier to use a pair of pliers to grab the locking slide to release the snare.
OK, you now have a live iguana in your hand. This is not the time to ask yourself “now what”? If your local government will take live iguanas off your hands, you are lucky. If not, you can drop them in a garbage can with a tight fitting lid. They can jump out of the standard 32 gallon garbage can so make sure the lid is secure.
I've also had good results using a Havahart #1089 trap (32" x 10" x 12"). Load it with banana, mango or lettuce and you might catch two at a time. I'm also using a smaller one (Havahart #1088) for the iguanas that are under two feet. The small trap will not work for large iguanas.
If you must euthanize them yourself, the only humane and legal way in Florida for a homeowner is freezing. You can drop them into a chest freezer. Freezing also makes it easier to dispose of them on garbage day. I am also looking into using bottled CO2 gas, connecting it to the same garbage can I collect them in. SEE UPDATE BELOW
There are other ways but most are too difficult for the homeowner. Decapitation is allowed but you must also pith them (scramble the brain). For many people decapitation may be the first choice after the iguanas eat their new landscaping.
You will have to check frequently (not necessarily here) to find the currently humane and legal methods to euthanize them.
I have tried using CO2 gas to euthanize the iguanas. It does work, most of the time but does not seem to be as humane as freezing. When I used CO2 gas, the iguanas thrashed around gasping for air. I would periodically add gas to the chamber to make sure they stayed "dead", but I did have one come back to life after lying motionless for over a day.
Freezing is now my prefered method for euthanizing iguanas. I think it is painless (might be uncomfortable but it happens to wild ones further north in Florida), inexpensive and convenient for the homeowner that is stuck dealing with this problem.
You can use a small chest freezer to do the job, but a larger freezer is only a few bucks more. If you have a freezer that will fit the large Havaheart trap, you won't have to handle a large aggressive iguana. Several neighbors with an iguana problem could have a large freezer in a location convenient to everyone quickly bringing the situation back to normal in your neighborhood.
I've had good results using a Havahart #1089 trap (32" x 10" x 12"). Load it with banana, mango or lettuce and you might catch two at a time. I'm also using a smaller one (Havahart #1088) for the iguanas that are under two feet. The small trap will not work for large iguanas.