Not sure if you're talking about moving them as in "moving from the tank for a few minutes" or "transporting in a car," lol, but here's what I do for both. I don't like to use nets since it's easy for them to get their fingers and toes stuck. I usually take a small bucket or lately I've been using a plastic shoebox (which I bought specifically for this purpose), stick it into the water on its side (slowly, so it doesn't create a strong current while filling up) and then very gently grab my axolotls around the body with my hand (after it's been WELL rinsed off) and guide them into the bucket, or with the more flighty ones, I kind of gently shoo them into the bucket. Sometimes I use food as a distraction or a "consolation prize" so they start to go into the bucket by choice. After it's in, you can slowly re-invert the bucket and lift it out of the tank. I would definitely recommend using some kind of lid at this point. It doesn't have to be super securely fastened, but it will help block out the light and keep them from jumping out.
If you are transporting by car (not recommended, but sometimes necessary), be sure to use a container that has COMPLETELY smooth insides, including the lid. There should be no protrusions, whether sharp or not. The lid must be secured and water-tight. Put the container on the floor, surround it with towels or blankets to keep it insulated and from moving around, blast the air-conditioning, and drive as slowly and smoothly as you can. I've done this several times for drives around 2 and a half hours. Be sure to bring along any equipment you will need to set up as soon as you arrive, including filter media. I usually keep this stuff in another container that is also filled with tank water in order to keep the bacteria alive. Again, I do not recommend traveling with an axolotl as it can be very stressful for them, but if you must, that's how I do it.