Welcome and congrats! Soon you will be getting the betta bug hehe, trust me :D
You will want to add in the water decholinator prior to putting your fish in his new home.
How do I introduce them to the new tank? I would float the cup in the new tank for 30 mins or so to get the temp even so it will be less stress for the little guy. Also, keep the lights on his tank dim/off for a while to keep him calm.
When do I feed them? Once or twice a day, very small amounts. They do beg for food and are big pigs when it comes to eating. Think of a lab puppy, food oriented. Don't let him fool you, he won't be starving. If he is an adult, ave 2in in body length, skipping one day a week will be good for him as well. Variety in food is great. So bettamin flakes, small pellets, frozen bloodworms and/or frozen brine shrimp will be loved. Freeze dried is good only for an occasional snack since they tend to bloat the fish and have no nutrients to them. Be aware that he may not eat up to a week or two after you get him, sometimes it takes them a bit to get comfy enough to eat. If you feel as if he needs to eat, can soak the pellets in garlic juice. It's the fish version of catnip lol. Also with pellets, if you see him spit them out a cpl times while eating, try presoaking them or smashing/cutting them up. Sometimes those pellets can be too large.
When and how should I clean the fish tank? I would suggest 1 50% water change and 1 50% substrate water change per week. On the substrate can do the stir/dip method to get as much you can out. Cupping him in his cup while you do so won't harm him, and would be better if you see him going crazy when you do the change. Always add in the dechlorinator in the tank every change, for full dose. Don't use soap on the tank or the deco, that can harm/kill. Some people may recommend 1 50% and 1 100% change, to me either is fine depending upon how dirty your guy gets.
And since I don't have a heater is there any way to maintain a correct temperature? Water changes, heat lamp, location. I would suggest a heater when/if you can though to help. http://www.amazon.com/Hydor-HEATER-A.../dp/B0006JLPFE[/url] is a good size. If you can't, at least get a thermometer so you can keep an eye on it and any fluctuations. Sometimes room temp is just right. They prefer 76-82F.
You said a few deco, they love hiding places, so if you can get some rock formation or cave, he'll love it, along with plants. With few things in the tank, they can get bored easily. So spoil away :)
Good luck with him! Any more questions feel free to ask, if you see anything wrong, don't hesitate to fill out the sticky and post in the emergency section of the forums. Oh, and want pics when you get him! :)
On a side note, make sure the filter doesn't push the water out too fast, they like it calm. There is a way to put a sponge in there to help keep it calm, but I don't know how to do it myself :(