To clean your betta fish's tank you should first remove the betta and then empty the gravel from the tank. The gravel should be put into a strainer while you go on scrubbing the walls of the tank using warm water and a brush. Finally, you should check for any residue and then return your betta fish with fresh water. To get more tips you can check this out http://www.wikihow.com/Clean-a-Betta-Fish-Tank.
Be sure that when you are cleaning the bowl don't use soap and if you do be sure to rinse really well because it can make your fish sick and when taking him out you could use a fish net but some fish get traumatized by the net so try to slowly dip in a little cup and try to get the fish out that way. Hope this helps :]