Originally Posted by DukeTheFish
( I didn't use soap because I didn't think that would be good for him)
Good, never use any soaps to clean his aquarium or anything that will go in his aquarium. Warm water will do just fine to rinse anything.
In such a small tank, you'll need to do very frequent water changes, like 50% a day. It's strange but the larger the tank, the fewer changes you have to do. If you can, you might want to consider upgrading your Duke to a tank that is 2.5 gallons or more someday. In the long run, it's less work for you and Duke will be happier.
Heat is another big issue. With luck, your local Petsmart should have a product like this Zoo Med Betta Bowl Heater.
This is a good heater for a small tank. Bettas come from tropical waters that are very warm so he'll need water temps around 78-80 degrees farenheit (25-26 degrees celsius) to thrive. With warm water, you'll see him start to move around more. Of course, if you plan on getting a bigger tank very soon (next week or so), hold off on the Zoo Med heater and get a nice 50w one.
I would definitely suggest also that you use a water conditioner like Seachem Prime. It's advertised to detoxify ammonia, which you may have more of since it's a small tank with no filter. It also will detoxify other things like heavy metals that can harm Duke. Prime may seem expensive at first but it's highly concentrated which means it will last a long time.
You said the NutraFin flakes were part of the kit you were sold? Then you haven't bought him food yet? I'd suggest pellets as they are easier to feed and won't mess up the water as much as flakes. There are several brands to choose from, too. Only feed him maybe 2 pellets about 3 times a day or he'll overeat. Bettas are little piggies when it comes to food.
You're on your way to being a great betta owner. Duke is lucky to have you.
And welcome to the forum.
One more thing: Get a thermometer so you can monitor the temperature. Water can heat up pretty fast so you want to make sure Duke's water isn't getting to warm there by the window. Even indirect sunlight can warm up pretty fast.