I have 10 gal tanks, so I don't usually have to take my Bettas out unless I'm doing a very big clean and then I use a small jug to scoop him out with some water at the same time. In smaller tanks and bowls it is kinder (and a lot easier) to take them out and put them in another container.
Personally, I would try to avoid nets if possible as Bettas, particularly males, have very delicate finnage and nets can cause a lot of damage if you're not very careful. I would use a cup or small jug to scoop him out of his tank or bowl and then either leave in there (securely covered, allowing air holes too) or take a bit more of the old water out and use another small bowl to put him in. If you cover whatever he's in to keep him dark it will help to reduce stress and prevent him from jumping. Some members have bettas that will just swim straight into their cup or jug when water changes are due!