Helped an Ohio biologist friend band forest birds decades ago, but nothing quite that small. Surprised me a bit that he used traps, too, instead of the mist nets used for woodcock.
The way he caught the hummingbirds was by putting a feeder inside a big cage/trap. Big meaning may be 1.5' to 2' cube. Sort of like catching minnows or crabs in a trap. They used two kinds. One pretty much exactly like a minnow trap where it's easy to get in but then they have a hard time finding their way back out. The other kind has a remote controlled door that they close when one flies in.
This particular park is all about bird watching. They have a bunch of feeders including a whole bunch of hummingbird feeders, flowers, etc. So the day they are trapping, they take down all the humming bird feeders and replace a few of them with the traps that have a feeder inside.
We went there last year or the year before to watch them band song birds. They used the mist nets for them.
The bands actually come in flat stamped sheets. As you know bands are numbered XXXX-YYYYY. The bands are so small, they can't fit the 4 digit prefix, so they are just a letter and the 5 numbers. He has a special pliers to take the flat band and bend it which he keeps them on safety pins. Just for size reference. He puts 20 bands on a small safety pin.
The oldest hummingbird that was recaptured was 9 years and 4 months if I remember correctly. He has personally recovered a couple of his bands that were over 8 years old. That seems like a very long time for such a little creature.