Everybody seems to mostly gloss over the subject of siphoning. Hard to find a detailed how-to here or anywhere else. And everybody has their own techniques with tips and tricks.
For me, it's less important to match the siphon to the tank size and more important to match it to the gravel/sand size. Too little power leaves the poop and food bits you're trying to siphon out. Too much power means you suck up the gravel until the siphon clogs. (Pinch the siphon tube and the gravel falls out; then go again. Gets to be a pain after a while.) Too much power can be dangerous to curious Betta. (Don't ask me how I know.)
I, and many of us, have experimented with different size tubing and pickup heads. The tubing size determines the volume per minute. The pickup head size determines the sucking power. You want just enough power to jostle the gravel around and loosen it up without sucking it into the siphon tube.
What works for me and my size gravel (less than 1/4 inch) is a 5/16 ID tube inserted through the bottom of a 1-inch diameter pill bottle. This size is about right to vacuum MY gravel and to change water on a 5 gal tank; not to slow, not too fast. And the suction is safe for my fish.
Learn to suck siphon; less stress on the fish.
1) Put the pickup near the bottom.
2) Leave a long enough piece of tube to sag below the tank.
3) Gently suck (kind of a reverse puff) on the tube from above tank level until the it's mostly full of water, without sucking the water into your mouth.(Practice,practice).
4) Put your finger over the output end tube, then put the output end of the tube into you wastewater bucket, which should be below tank level.. After a little practice you'll get the siphon going first try every time and never spill a drop.
5) Stir the gravel around gently with the pickup end and watch the debris get sucked into the tube. Keep it away from your curious fish.
For simple water changes without vacuuming the gravel, it's fine (if somewhat tedious and messy) to just dip the water out with a cup.
Pouring fresh, conditioned water into the tank takes a little patience to avoid stirring up the bottom, knocking over plants and things, getting those annoying tiny bubbles all over everything and scaring the fish. I put my (clean) hand down into the tank and pour the water over it without splashing . Some people pour into a clean bowl on the bottom. I finish filling the last couple of quarts by pouring slowly over the rim and let my fish play in the waterfall. Crazy Betta, I know, I know.
Other people have other methods and refinements. I'd like to see a thread devoted to this subject.