I've posted this on a couple of other (betta) boards and thought I'd share in case it helps anyone here!
I can't bring myself to net my bettas as they seem so disoriented and quite upset, being pulled into the air and then suddenly put somewhere else. The method I had always used was partially submerging a clear cup (clear seemed to be less distressing than a cup they couldn't see out of) in the water with the cup's rim just at the surface. When the betta would swim near the cup, I'd dunk it into the water, sucking the betta in.
But even this seemed distressing to my fish, and when the cup was put in the water, they would swim to the bottom of the tank and try to avoid it. I was careful to never ambush them when they came up for air, and so it would take a LONG time to catch them!
So I decided that this was too distressing for him (and me!) and I set out to train him to swim into the cup on his own!
Here were the steps, starting from the day I brought him home:
(1) First, he wouldn't come to my hand to be fed, so I made a routine of holding the food at the water's surface between my fingers for a second before dropping it in. He saw this and came to associate my hand near the water with food;
(2) Soon he would see my hand approaching the water with food and would swim to it, having established the pattern;
(3) Once he would swim to my hand, I would move my hand around over the water's surface, encouraging him to follow it before dropping the food in;
(4) Then, after a few feedings with him following the food, stopped dropping the food in after letting him chase my fingers, instead holding onto the food just above the water's surface. he quickly figured out that he could jump to get the food, and did so;
(5) Once he was this comfortable with taking food from my hand and being near my hand, I started submerging the clear mug that I would catch him in in the water. First I did so without the food, and just let him investigate the mug, holding the cup still and half submerged into the water so that he could swim in if he wished. He didn't, but he swam right up to the edge of it and hovered there, seemingly testing if he would be sucked in as usual, which he of course was not;
(6) Finally, when he was comfortable with the cup's presence in the water, I submerged the cup at feeding time, and had him follow my finger into the cup. He went in quite willingly and I immediately gave him his food, which he ate in the cup. After doing this a few times, I started gently lifting the cup out of the water (with him in it) before feeding him, and he didn't try to escape as I slowly turned the cup right-side up and lifted it from the water.
Now, when I put the cup into the tank, he doesn't even need to follow my finger anymore, he just swims in on his own, anticipating food! He'll even try to get back into the cup again after he's been fed and released, thinking if he can get back in he'll be fed again :p
I'm trying to get a video of him doing this. :D
Hope this is helpful to some of you - I think bettas are WAY too smart, and they're capable of so much more than this. Best of luck with your fishies!