Changing the water is a bit different than cleaning the whole tank,
To do a good water change, get yourself a gravel vacume siphon. This is basically a silcone tube with a 1" or 2" clear plastic tube at one end. Most hex tanks use undergravel filters, and this vacume will help you remove most of the waste (feces, food) that drops into the gravel.
Leave the betta in the tank unless you are doing a 100% water change (anything under 1 gallon) If you need to remove him, put him in a clean bowl (no soap residue) using his old tank water while you clean the tank.
I change 25 to 30% of my betta tanks water once a week. First, I pre-treat (chlorine/chloramine remover) the water and let it sit out one day so it gets to room temperature. Always treat the water before you make any changes (Aqua Plus or simular). The water should be about the same temperature as the tank water. I use a floating thermeter ($2.00 at Walmart) to test it, but your finger would be just as good. I turn off any air pumps or filters, use the siphon vacume (put a bucket on the floor below the tank, put the big end in the tank, suck on the small end till the water starts flowing and try to stop before you get a mouthful) and suck out the gravel. You will see the gravel rise up a little, which is OK, and all the loose debris will flow up the tube into your waste bucket.
Add the new water slowly, pouring it against the side or ontop of the filter so it will not disturb your fish/gravel too much. Turn the filters and air pumps back on and your done!
If you need to do a full water change, take the betta out (see above), pour some of the old water into a bucket, move all the gravel into the old water bucket, and remove everything else. You can clean the tank using a water/vinegar solution, and wipe down all the sides and decorations and rinse really well. Use the old tank water to rinse the gravel out, and put it back in the clean tank. I don't sanitize my gravel, I want to keep the good bacteria alive.
Add decorations and then the new treated water to the tank (same temperature as old water), then put the betta back in.
This is also a good time to test your water (old and new) for pH, ammonia and nitrite if you have a test kit.