Welcome to the forum and betta keeping.
okay, temp is recommended to be 76-80 degrees fahrenheit, to do this, you might want to get a heater to keep the temperatures a constant temperature, and a thermometer to moniter the temperatures.
feeding (pellets) 2-3 pellets twice a day. Make sure to soak the pellets completely. When buying food, make sure the first ingredient is some sort of meat (shrimp or fish meal)
I personally believe you are safer off leaving your betta be. Some bettas are little adorable devils that kill anything you put in his/her tank, others are little lambs (I have one of each XD )
The safest tankmates would be shrimps and snails. Even with those, you risk the shrimps being eaten... Nothing less than 5 gallons for snails and or shrimps with a betta fish. Nothing less than 10 gallons for a small school of fish. The reason you want such large tanks is because you want to be able to provide space so the other fish can escape and hide from your betta if he decides to go nuts. Good fish would be harlequin rasboras or neon tetras.
* Oh, this is important. Depending on how tall or long your tank is, you may or may not be able to keep many tank mates with your betta. The more air surface your tank has means the more you can stock.
Putting a mirror infront of your betta for a minute or two each day will make him flare like crazy and exercise, which won't hurt. However, beware doing it too long, because it could stress him.
Cleaning the tank: You can get a filter, but you'll want to make sure it doesn't toss your betta around too much, basically, make sure it is a very slow flow, because too much current is bad for bettas because of their long fins. If you decide to cycle (http://www.fishlore.com/NitrogenCycle.htm
) your water changes will be significantly less. If you don't, just be sure to keep up with water changes.
Water: If you are using tap water, be sure to condition it so all the ammonia, chlorine, and heavy metals are detoxified. Just letting water sit isn't enough. If you are on well water, I've heard from people no conditioning is necessary.
You've got a 10 gallon, so if you want, you can load it with a bunch of plants and possibly a few hiding spots for your betta, so he has some place to hide in if he wants.
Also, I'd like to add that bettas are beautiful fish that bond well with their owners and are relatively hardy, so they are sort of forgiving to new owners' mistakes :)